Version:	1.3.5
Date:	2025-01-12
Title:	Optimally Robust Estimation
Description:	R infrastructure for optimally robust estimation in general smoothly parameterized models using S4 classes and methods as described Kohl, M., Ruckdeschel, P., and Rieder, H. (2010), <doi:10.1007/s10260-010-0133-0>, and in Rieder, H., Kohl, M., and Ruckdeschel, P. (2008), <doi:10.1007/s10260-007-0047-7>.
Depends:	R(≥ 3.4), methods, distr(≥ 2.8.0), distrEx(≥ 2.8.0), distrMod(≥ 2.8.1), RandVar(≥ 1.2.0), RobAStBase(≥ 1.2.0)
Imports:	startupmsg(≥ 1.0.0), MASS, stats, graphics, utils, grDevices
Suggests:	RobLox
ByteCompile:	yes
License:	LGPL-3
URL:	http://robast.r-forge.r-project.org/
Encoding:	UTF-8
LastChangedDate:	{$LastChangedDate: 2025-01-12 01:50:47 +0100 (So, 12. Jan 2025) $}
LastChangedRevision:	{$LastChangedRevision: 1324 $}
VCS/SVNRevision:	1323
NeedsCompilation:	no
Packaged:	2025-01-12 15:08:33 UTC; kohlm
Author:	Matthias Kohl [cre, cph], Mykhailo Pupashenko [ctb] (contributed wrapper functions for diagnostic plots), Gerald Kroisandt [ctb] (contributed testing routines), Peter Ruckdeschel [aut, cph]
Maintainer:	Matthias Kohl <Matthias.Kohl@stamats.de>
Repository:	CRAN
Date/Publication:	2025-01-15 12:00:02 UTC

Optimally robust estimation

Description

Optimally robust estimation in general smoothly parameterized models using S4 classes and methods.

Details

Package versions

Note: The first two numbers of package versions do not necessarily reflect package-individual development, but rather are chosen for the RobAStXXX family as a whole in order to ease updating "depends" information.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
Maintainer: Matthias Kohl matthias.kohl@stamats.de

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf. M. Kohl, P. Ruckdeschel, and H. Rieder (2010). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Statistical Methods and Applications 19(3): 333-354. doi:10.1007/s10260-010-0133-0. H. Rieder (1994): Robust Asymptotic Statistics. Springer. doi:10.1007/978-1-4684-0624-5 H. Rieder, M. Kohl, and P. Ruckdeschel (2008). The Costs of Not Knowing the Radius. Statistical Methods and Applications 17(1): 13-40. doi:10.1007/s10260-007-0047-7 P. Ruckdeschel (2005). Optimally One-Sided Bounded Influence Curves. Mathematical Methods of Statistics 14(1), 105-131. P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

See Also

distr-package, distrEx-package, distrMod-package, RandVar-package, RobAStBase-package

Examples

## don't test to reduce check time on CRAN

library(ROptEst)
## Example: Rutherford-Geiger (1910); cf. Feller~(1968), Section VI.7 (a)
x <- c(rep(0, 57), rep(1, 203), rep(2, 383), rep(3, 525), rep(4, 532), 
       rep(5, 408), rep(6, 273), rep(7, 139), rep(8, 45), rep(9, 27), 
       rep(10, 10), rep(11, 4), rep(12, 0), rep(13, 1), rep(14, 1))
## ML-estimate from package distrMod
MLest <- MLEstimator(x, PoisFamily())
MLest
## confidence interval based on CLT
confint(MLest)
## compute optimally (w.r.t to MSE) robust estimator (unknown contamination)
robEst <- roptest(x, PoisFamily(), eps.upper = 0.1, steps = 3)
estimate(robEst)
## check influence curve
pIC(robEst)
checkIC(pIC(robEst))
## plot influence curve
plot(pIC(robEst))
## confidence interval based on LAN - neglecting bias
confint(robEst)
## confidence interval based on LAN - including bias
confint(robEst, method = symmetricBias())

Wrapper function for cniperPointPlot - Computation and Plot of Cniper Contamination and Cniper Points

Description

The wrapper CniperPointPlot (capital C!) takes most of arguments to the cniperPointPlot (lower case c!) function by default and gives a user possibility to run the function with low number of arguments.

Usage

  CniperPointPlot(fam, ...,
    lower = getdistrOption("DistrResolution"),
    upper = 1 - getdistrOption("DistrResolution"),
    with.legend = TRUE, rescale = FALSE, withCall = TRUE)

Arguments

Value

invisible(NULL)

Details

Calls cniperPointPlot with suitably chosen defaults; if withCall == TRUE, the call to cniperPointPlot is returned.

Examples

L2fam <- NormLocationScaleFamily()
CniperPointPlot(fam=L2fam, main = "Normal location and scale", 
                lower = 0, upper = 2.5, withCall = FALSE)

ORobEstimate-class.

Description

Class of optimally robust asymptotically linear estimates.

Objects from the Class

Objects can be created by calls of the form new("ORobEstimate", ...). More frequently they are created as results of functions roptest, MBREstimator, RMXEstimator, or OMSEstimator.

Slots

name

Object of class "character": name of the estimator. [*]

estimate

Object of class "ANY": estimate. [*]

estimate.call

Object of class "call": call by which estimate was produced. [*]

samplesize

object of class "numeric" — the samplesize (only complete cases are counted) at which the estimate was evaluated. [*]

completecases:

object of class "logical" — complete cases at which the estimate was evaluated. [*]

asvar

object of class "OptionalNumericOrMatrix" which may contain the asymptotic (co)variance of the estimator. [*]

asbias

Optional object of class "numeric": asymptotic bias. [*]

pIC

Optional object of class InfluenceCurve: influence curve. [*]

nuis.idx

object of class "OptionalNumeric": indices of estimate belonging to the nuisance part. [*]

fixed

object of class "OptionalNumeric": the fixed and known part of the parameter. [*]

steps

Object of class "integer": number of steps. [*]

Infos

object of class "matrix" with two columns named method and message: additional informations. [*]

trafo

object of class "list": a list with components fct and mat (see below). [*]

untransformed.estimate:

Object of class "ANY": untransformed estimate. [*]

untransformed.asvar:

object of class "OptionalNumericOrMatrix" which may contain the asymptotic (co)variance of the untransformed estimator. [*]

pICList

Optional object of class "OptionalpICList": the list of (intermediate) (partial) influence curves used; only filled when called from ORobEstimator with argument withPICList==TRUE. [*]

ICList

Optional object of class "OptionalpICList": the list of (intermediate) (total) influence curves used; only filled when called from ORobEstimator with argument withICList==TRUE. [*]

start

The argument start — of class "StartClass" used in call to ORobEstimator. [*]

startval

Object of class matrix: the starting value with which the k-step Estimator was initialized (in p-space / transformed). [*]

ustartval

Object of class matrix: the starting value with which the k-step Estimator was initialized (in k-space / untransformed). [*]

ksteps

Object of class "OptionalMatrix": the intermediate estimates (in p-space) for the parameter; only filled when called from ORobEstimator. [*]

uksteps

Object of class "OptionalMatrix": the intermediate estimates (in k-space) for the parameter; only filled when called from ORobEstimator. [*]

robestcall

Object of class "OptionalCall", i.e., a call or NULL: only filled when called from roptest. [*]

roptestcall

Object of class "OptionalCall", i.e., a call or NULL: only filled when called from roptest, MBREstimator, RMXEstimator, or OMSEstimator.

Extends

Class "kStepEstimate", directly.
Class "ALEstimate" and class "Estimate", by class "kStepstimate". All slots and methods marked with [*] are inherited.

Methods

steps

signature(object = "ORobEstimate"): accessor function for slot steps. [*]

ksteps

signature(object = "ORobEstimate"): accessor function for slot ksteps; has additional argument diff, defaulting to FALSE; if the latter is TRUE, the starting value from slot startval is prepended as first column; otherwise we return the corresponding increments in each step. [*]

uksteps

signature(object = "ORobEstimate"): accessor function for slot uksteps; has additional argument diff, defaulting to FALSE; if the latter is TRUE, the starting value from slot ustartval is prepended as first column; otherwise we return the corresponding increments in each step. [*]

start

signature(object = "ORobEstimate"): accessor function for slot start. [*]

startval

signature(object = "ORobEstimate"): accessor function for slot startval. [*]

ustartval

signature(object = "ORobEstimate"): accessor function for slot startval. [*]

ICList

signature(object = "ORobEstimate"): accessor function for slot ICList. [*]

pICList

signature(object = "ORobEstimate"): accessor function for slot pICList. [*]

robestCall

signature(object = "ORobEstimate"): accessor function for slot robestCall. [*]

roptestCall

signature(object = "ORobEstimate"): accessor function for slot roptestCall.

timings

signature(object = "ORobEstimate"): accessor function for attribute "timings". with additional argument withKStep defaulting to FALSE; in case argument withKStep==TRUE, the return value is a list with items timings and kStepTimings combining the two timing informaion attributes.

kSteptimings

signature(object = "ORobEstimate"): accessor function for attribute "timings".

show

signature(object = "ORobEstimate"): a show method; [*]

Author(s)

Peter Ruckdeschel Peter.Ruckdeschel@uni-oldenburg.de

See Also

ALEstimate-class, kStepEstimate-class

Optimally robust estimation: RMXE, OMSE, MBRE, and OBRE

Description

These are wrapper functions to 'roptest' to compute optimally robust estimates, more specifically RMXEs, OMSEs, MBREs, and OBREs, for L2-differentiable parametric families via k-step construction.

Usage

RMXEstimator(x, L2Fam, fsCor = 1, initial.est, neighbor = ContNeighborhood(),
             steps = 1L, distance = CvMDist, startPar = NULL, verbose = NULL,
             OptOrIter = "iterate", useLast = getRobAStBaseOption("kStepUseLast"),
             withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
             IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
             withICList = getRobAStBaseOption("withICList"),
             withPICList = getRobAStBaseOption("withPICList"), na.rm = TRUE,
             initial.est.ArgList, ..., withLogScale = TRUE, ..withCheck=FALSE,
             withTimings = FALSE, withMDE = NULL, withEvalAsVar = NULL,
             withMakeIC = FALSE, modifyICwarn = NULL, E.argList = NULL,
             diagnostic = FALSE)
OMSEstimator(x, L2Fam, eps=0.5, fsCor = 1, initial.est, neighbor = ContNeighborhood(),
             steps = 1L, distance = CvMDist, startPar = NULL, verbose = NULL,
             OptOrIter = "iterate", useLast = getRobAStBaseOption("kStepUseLast"),
             withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
             IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
             withICList = getRobAStBaseOption("withICList"),
             withPICList = getRobAStBaseOption("withPICList"), na.rm = TRUE,
             initial.est.ArgList, ..., withLogScale = TRUE, ..withCheck=FALSE,
             withTimings = FALSE, withMDE = NULL, withEvalAsVar = NULL,
             withMakeIC = FALSE, modifyICwarn = NULL, E.argList = NULL,
             diagnostic = FALSE)
OBREstimator(x, L2Fam, eff=0.95, fsCor = 1, initial.est, neighbor = ContNeighborhood(),
             steps = 1L, distance = CvMDist, startPar = NULL, verbose = NULL,
             OptOrIter = "iterate", useLast = getRobAStBaseOption("kStepUseLast"),
             withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
             IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
             withICList = getRobAStBaseOption("withICList"),
             withPICList = getRobAStBaseOption("withPICList"), na.rm = TRUE,
             initial.est.ArgList, ..., withLogScale = TRUE, ..withCheck=FALSE,
             withTimings = FALSE, withMDE = NULL, withEvalAsVar = NULL,
             withMakeIC = FALSE, modifyICwarn = NULL, E.argList = NULL,
             diagnostic = FALSE)
MBREstimator(x, L2Fam, fsCor = 1, initial.est, neighbor = ContNeighborhood(),
             steps = 1L, distance = CvMDist, startPar = NULL, verbose = NULL,
             OptOrIter = "iterate", useLast = getRobAStBaseOption("kStepUseLast"),
             withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
             IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
             withICList = getRobAStBaseOption("withICList"),
             withPICList = getRobAStBaseOption("withPICList"), na.rm = TRUE,
             initial.est.ArgList, ..., withLogScale = TRUE, ..withCheck=FALSE,
             withTimings = FALSE, withMDE = NULL, withEvalAsVar = NULL,
             withMakeIC = FALSE, modifyICwarn = NULL, E.argList = NULL,
             diagnostic = FALSE)

Arguments

Details

The functions compute optimally robust estimator for a given L2 differentiable parametric family; more specifically they are RMXEs, OMSEs, MBREs, and OBREs. The computation uses a k-step construction with an appropriate initial estimate; cf. also kStepEstimator. Valid candidates are e.g. Kolmogorov(-Smirnov) or von Mises minimum distance estimators (default); cf. Rieder (1994) and Kohl (2005).

For OMSE, i.e., the asymptotically linear estimator with minimax mean squared error on this neighborhood of given size, the amount of gross errors (contamination) is assumed to be known, and is specified by eps. The radius of the corresponding infinitesimal contamination neighborhood is obtained by multiplying eps by the square root of the sample size.

If the amount of gross errors (contamination) is unknown, RMXE should be used, i.e., the radius-minimax estimator in the sense of Rieder et al. (2001, 2008), respectively Section 2.2 of Kohl (2005) is returned.

The OBRE, i.e., the optimal bias-robust (asymptotically linear) estimator; (terminology due to Hampel et al (1985)), expects an efficiency loss (at the ideal model) to be specified and then, according to an (asymptotic) Anscombe criterion computes the the bias bound achieving this efficiency loss.

The MBRE, i.e., the most bias-robust (asymptotically linear) estimator; (terminology due to Hampel et al (1985)), uses the influence curve with minimal possible bias bound, hence minimaxes bias on these neighborhoods (in an infinitesimal sense)..

Finite-sample and higher order results suggest that the asymptotically optimal procedure is to liberal. Using fsCor the radius can be modified - as a rule enlarged - to obtain a more conservative estimate. In case of normal location and scale there is function finiteSampleCorrection which returns a finite-sample corrected (enlarged) radius based on the results of large Monte-Carlo studies.

The default value of argument useLast is set by the global option kStepUseLast which by default is set to FALSE. In case of general models useLast remains unchanged during the computations. However, if slot CallL2Fam of IC generates an object of class "L2GroupParamFamily" the value of useLast is changed to TRUE. Explicitly setting useLast to TRUE should be done with care as in this situation the influence curve is re-computed using the value of the one-step estimate which may take quite a long time depending on the model.

If useLast is set to TRUE the computation of asvar, asbias and IC is based on the k-step estimate.

All these estimators are realized as wrappers to function roptest.

Timings for the steps run through in these estimators are available in attributes timings, and for the step of the kStepEstimator in kStepTimings.

One may also use the arguments startCtrl, startICCtrl, and kStepCtrl of function robest. This allows for individual settings of E.argList, withEvalAsVar, and withMakeIC for the different steps. If any of the three arguments startCtrl, startICCtrl, and kStepCtrl is used, the respective attributes set in the correspondig argument are used and, if colliding with arguments directly passed to the estimator function, the directly passed ones are ignored.

Diagnostics on the involved integrations are available if argument diagnostic is TRUE. Then there are attributes diagnostic and kStepDiagnostic attached to the return value, which may be inspected and assessed through showDiagnostic and getDiagnostic.

Value

Object of class "kStepEstimate". In addition, it has an attribute "timings" where computation time is stored.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

Kohl, M. and Ruckdeschel, P. (2010): R package distrMod: Object-Oriented Implementation of Probability Models. J. Statist. Softw. 35(10), 1–27. doi:10.18637/jss.v035.i10.

Kohl, M. and Ruckdeschel, P., and Rieder, H. (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333–354. doi:10.1007/s10260-010-0133-0.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer. doi:10.1007/978-1-4684-0624-5.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2008) The Costs of not Knowing the Radius. Statistical Methods and Applications 17(1) 13-40. doi:10.1007/s10260-007-0047-7.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2001) The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under doi:10.18452/3638

See Also

roptest, robest, roblox, L2ParamFamily-class UncondNeighborhood-class, RiskType-class

Examples

#############################
## 1. Binomial data
#############################
## generate a sample of contaminated data
set.seed(123)
ind <- rbinom(100, size=1, prob=0.05)
x <- rbinom(100, size=25, prob=(1-ind)*0.25 + ind*0.9)

## ML-estimate
MLE.bin <- MLEstimator(x, BinomFamily(size = 25))
## compute optimally robust estimators
OMSE.bin <- OMSEstimator(x, BinomFamily(size = 25), steps = 3)
MBRE.bin <- MBREstimator(x, BinomFamily(size = 25), steps = 3)
estimate(MLE.bin)
estimate(MBRE.bin)
estimate(OMSE.bin)

  ## to reduce time load at CRAN tests
RMXE.bin <- RMXEstimator(x, BinomFamily(size = 25), steps = 3)
OBRE.bin <- OBREstimator(x, BinomFamily(size = 25), steps = 3)
estimate(RMXE.bin)
estimate(OBRE.bin)

  ## to reduce time load at CRAN tests
#############################
## 2. Poisson data
#############################

## Example: Rutherford-Geiger (1910); cf. Feller~(1968), Section VI.7 (a)
x <- c(rep(0, 57), rep(1, 203), rep(2, 383), rep(3, 525), rep(4, 532),
       rep(5, 408), rep(6, 273), rep(7, 139), rep(8, 45), rep(9, 27),
       rep(10, 10), rep(11, 4), rep(12, 0), rep(13, 1), rep(14, 1))

## ML-estimate
MLE.pois <- MLEstimator(x, PoisFamily())
OBRE.pois <- OBREstimator(x, PoisFamily(), steps = 3)
OMSE.pois <- OMSEstimator(x, PoisFamily(), steps = 3)
MBRE.pois <- MBREstimator(x, PoisFamily(), steps = 3)
RMXE.pois <- RMXEstimator(x, PoisFamily(), steps = 3)
estimate(MLE.pois)
estimate(OBRE.pois)
estimate(RMXE.pois)
estimate(MBRE.pois)
estimate(OMSE.pois)


 ## to reduce time load at CRAN tests
#############################
## 3. Normal (Gaussian) location and scale
#############################
## 24 determinations of copper in wholemeal flour
library(MASS)
data(chem)

MLE.n <- MLEstimator(chem, NormLocationScaleFamily())
MBRE.n <- MBREstimator(chem, NormLocationScaleFamily(), steps = 3)
OMSE.n <- OMSEstimator(chem, NormLocationScaleFamily(), steps = 3)
OBRE.n <- OBREstimator(chem, NormLocationScaleFamily(), steps = 3)
RMXE.n <- RMXEstimator(chem, NormLocationScaleFamily(), steps = 3)

estimate(MLE.n)
estimate(MBRE.n)
estimate(OMSE.n)
estimate(OBRE.n)
estimate(RMXE.n)

Generating function for asAnscombe-class

Description

Generates an object of class "asAnscombe".

Usage

asAnscombe(eff = .95, biastype = symmetricBias(), normtype = NormType())

Arguments

Value

Object of class asAnscombe

Author(s)

Peter Ruckdeschel peter.ruckdeschel@fraunhofer.itwm.de

References

F.J. Anscombe (1960). Rejection of Outliers. Technometrics 2(2): 123-146. doi:10.1080/00401706.1960.10489888.

F. Hampel et al. (1986). Robust Statistics. The Approach Based on Influence Functions. New York: Wiley. doi:10.1002/9781118186435.

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

H. Rieder (1994). Robust Asymptotic Statistics. Springer. doi:10.1007/978-1-4684-0624-5.

See Also

asAnscombe-class

Examples

asAnscombe()

## The function is currently defined as
function(eff = .95, biastype = symmetricBias(), normtype = NormType()){ 
    new("asAnscombe", eff = eff, biastype = biastype, normtype = normtype) }

Asymptotic Anscombe risk

Description

Class of asymptotic Anscombe risk which is the ARE (asymptotic relative efficiency) in the ideal model obtained by an optimal bias robust IC .

Objects from the Class

Objects can be created by calls of the form new("asAnscombe", ...). More frequently they are created via the generating function asAnscombe.

Slots

type

Object of class "character": “optimal bias robust IC (OBRI) for given ARE (asymptotic relative efficiency)”.

eff

Object of class "numeric": given ARE (asymptotic relative efficiency) to be attained in the ideal model.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

Extends

Class "asRiskwithBias", directly.
Class "asRisk", by class "asRiskwithBias". Class "RiskType", by class "asRisk".

Methods

eff

signature(object = "asAnscombe"): accessor function for slot eff.

show

signature(object = "asAnscombe")

Author(s)

Peter Ruckdeschel peter.ruckdeschel@fraunhofer.itwm.de

References

F.J. Anscombe (1960). Rejection of Outliers. Technometrics 2(2): 123-146. doi:10.1080/00401706.1960.10489888.

F. Hampel et al. (1986). Robust Statistics. The Approach Based on Influence Functions. New York: Wiley. doi:10.1002/9781118186435.

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

H. Rieder (1994). Robust Asymptotic Statistics. Springer. doi:10.1007/978-1-4684-0624-5.

See Also

asRisk-class, asAnscombe

Examples

new("asAnscombe")

Generating function for asMSE-class

Description

Generates an object of class "asMSE".

Usage

asL1(biastype = symmetricBias(), normtype = NormType())

Arguments

Value

Object of class "asMSE"

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

See Also

asL1-class, asMSE, asL4

Examples

asL1()

## The function is currently defined as
function(biastype = symmetricBias(), normtype = NormType()){ 
         new("asL1", biastype = biastype, normtype = normtype) }

Asymptotic mean absolute error

Description

Class of asymptotic mean absolute error.

Objects from the Class

Objects can be created by calls of the form new("asL1", ...). More frequently they are created via the generating function asL1.

Slots

type

Object of class "character": “asymptotic mean square error”.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

normtype

Object of class "NormType": norm in which a multivariate parameter is considered

Extends

Class "asGRisk", directly.
Class "asRiskwithBias", by class "asGRisk".
Class "asRisk", by class "asRiskwithBias".
Class "RiskType", by class "asGRisk".

Methods

No methods defined with class "asL1" in the signature.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

See Also

asGRisk-class, asMSE, asMSE-class, asL4-class, asL1

Examples

new("asMSE")

Generating function for asL4-class

Description

Generates an object of class "asL4".

Usage

asL4(biastype = symmetricBias(), normtype = NormType())

Arguments

Value

Object of class "asL4"

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

See Also

asL4-class, asMSE, asL1

Examples

asL4()

## The function is currently defined as
function(biastype = symmetricBias(), normtype = NormType()){ 
         new("asL4", biastype = biastype, normtype = normtype) }

Asymptotic mean power 4 error

Description

Class of asymptotic mean power 4 error.

Objects from the Class

Objects can be created by calls of the form new("asL4", ...). More frequently they are created via the generating function asL4.

Slots

type

Object of class "character": “asymptotic mean square error”.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

normtype

Object of class "NormType": norm in which a multivariate parameter is considered

Extends

Class "asGRisk", directly.
Class "asRiskwithBias", by class "asGRisk".
Class "asRisk", by class "asRiskwithBias".
Class "RiskType", by class "asGRisk".

Methods

No methods defined with class "asL4" in the signature.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

See Also

asGRisk-class, asMSE, asMSE-class, asL1-class, asL4

Examples

new("asMSE")

Methods for Checking and Making ICs

Description

Particular methods for checking centering and Fisher consistency of ICs, resp. making an IC out of an IC possibly violating the conditions so far.

Usage

## S4 method for signature 'ContIC,L2ParamFamily'
checkIC(IC, L2Fam, out = TRUE,
              forceContICMethod = FALSE, ..., diagnostic = FALSE)
## S4 method for signature 'ContIC,L2ParamFamily'
makeIC(IC, L2Fam,
              forceContICMethod = FALSE, ..., diagnostic = FALSE)

Arguments

Details

In checkIC, the precisions of the centering and the Fisher consistency are computed. makeIC affinely transforms a given IC (not necessarily satisfying the centering and Fisher consistency condition so far) such that after this transformation it becomes an IC (satisfying the conditions). Here particular methods for ICs of class ContIC are provided using the particular structure of this class which allows for speed up in certain cases.

Value

The maximum deviation from the IC properties is returned.

Author(s)

Peter Ruckdeschel Peter.Ruckdeschel@uni-oldenburg.de

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

M. Kohl, P. Ruckdeschel, and H. Rieder (2010). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Statistical Methods and Applications 19(3): 333-354. doi:10.1007/s10260-010-0133-0.

H. Rieder (1994): Robust Asymptotic Statistics. Springer. doi:10.1007/978-1-4684-0624-5

See Also

L2ParamFamily-class, IC-class

Examples

IC1 <- new("IC")
checkIC(IC1)

Functions for Computation and Plot of Cniper Contamination and Cniper Points.

Description

These functions and their methods can be used to determine cniper contamination as well as cniper points. That is, under which (Dirac) contamination is the risk of one procedure larger than the risk of some other procedure.

Usage

cniperCont(IC1, IC2, data = NULL, ...,
           neighbor, risk, lower=getdistrOption("DistrResolution"),
           upper=1-getdistrOption("DistrResolution"), n = 101,
           with.automatic.grid = TRUE, scaleX = FALSE, scaleX.fct,
           scaleX.inv, scaleY = FALSE, scaleY.fct = pnorm, scaleY.inv=qnorm,
           scaleN = 9, x.ticks = NULL, y.ticks = NULL, cex.pts = 1,
           cex.pts.fun = NULL, col.pts = par("col"), pch.pts = 19,
           cex.npts = 0.6, cex.npts.fun = NULL, col.npts = "red", pch.npts = 20,
           jit.fac = 1, jit.tol = .Machine$double.eps, with.lab = FALSE,
           lab.pts = NULL, lab.font = NULL, alpha.trsp = NA, which.lbs = NULL,
           which.Order  = NULL, which.nonlbs = NULL, attr.pre = FALSE,
           return.Order = FALSE, withSubst = TRUE)

cniperPoint(L2Fam, neighbor, risk, lower, upper)

cniperPointPlot(L2Fam, data=NULL, ..., neighbor, risk= asMSE(),
                        lower=getdistrOption("DistrResolution"),
                        upper=1-getdistrOption("DistrResolution"), n = 101,
                        withMaxRisk = TRUE, with.automatic.grid = TRUE,
                           scaleX = FALSE, scaleX.fct, scaleX.inv,
                           scaleY = FALSE, scaleY.fct = pnorm, scaleY.inv=qnorm,
                           scaleN = 9, x.ticks = NULL, y.ticks = NULL,
                           cex.pts = 1, cex.pts.fun = NULL, col.pts = par("col"),
                           pch.pts = 19,
                           cex.npts = 1, cex.npts.fun = NULL, col.npts = par("col"),
                           pch.npts = 19,
                           jit.fac = 1, jit.tol = .Machine$double.eps,
                           with.lab = FALSE,
                           lab.pts = NULL, lab.font = NULL, alpha.trsp = NA,
                           which.lbs = NULL, which.nonlbs = NULL,
                           which.Order  = NULL, attr.pre = FALSE, return.Order = FALSE,
                           withSubst = TRUE, withMakeIC = FALSE)

Arguments

Details

In case of cniperCont the difference between the risks of two ICs is plotted.

The function cniperPoint can be used to determine cniper points. That is, points such that the optimally robust estimator has smaller minimax risk than the classical optimal estimator under contamination with Dirac measures at the cniper points.

As such points might be difficult to find, we provide the function cniperPointPlot which can be used to obtain a plot of the risk difference; in this function the usual arguments for plot can be used. For arguments col, lwd, vectors can be used; then the first coordinate is taken for the curve, the second one for the balancing line. For argument lty, a list can be used; its first component is then taken for the curve, the second one for the balancing line.

If argument withSubst is TRUE, in all title and axis lable arguments of cniperCont and cniperPointPlot, the following patterns are substituted:

"%C"

class of argument L2Fam (for cniperPointPlot)

"%A"

deparsed argument L2Fam (for cniperPointPlot)

"%C1"

class of argument IC1 (for cniperCont)

"%A1"

deparsed argument IC1 (for cniperCont)

"%C2"

class of argument IC2 (for cniperCont)

"%A2"

deparsed argument IC2 (for cniperCont)

"%D"

time/date-string when the plot was generated

For more details about cniper contamination and cniper points we refer to Section~3.5 of Kohl et al. (2008) as well as Ruckdeschel (2004) and the Introduction of Kohl (2005).

Value

The cniper point is returned by cniperPoint. In case of cniperPointPlot, we return an S3 object of class c("plotInfo","DiagnInfo"), i.e., a list containing the information needed to produce the respective plot, which at a later stage could be used by different graphic engines (like, e.g. ggplot) to produce the plot in a different framework. A more detailed description will follow in a subsequent version.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

M. Kohl, P. Ruckdeschel, and H. Rieder (2010). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Statistical Methods and Applications 19(3): 333-354. doi:10.1007/s10260-010-0133-0.

P. Ruckdeschel (2004). Higher Order Asymptotics for the MSE of M-Estimators on Shrinking Neighborhoods. Unpublished Manuscript.

Examples

## cniper contamination
P <- PoisFamily(lambda = 4)
RobP1 <- InfRobModel(center = P, neighbor = ContNeighborhood(radius = 0.1))
IC1 <- optIC(model=RobP1, risk=asMSE())
RobP2 <- InfRobModel(center = P, neighbor = ContNeighborhood(radius = 1))
IC2 <- optIC(model=RobP2, risk=asMSE())
cniperCont(IC1 = IC1, IC2 = IC2,
           neighbor = ContNeighborhood(radius = 0.5), 
           risk = asMSE(),
           lower = 0, upper = 8, n = 101)

## cniper point plot
cniperPointPlot(P, neighbor = ContNeighborhood(radius = 0.5), 
                risk = asMSE(), lower = 0, upper = 10)

## Don't run to reduce check time on CRAN

## cniper point
cniperPoint(P, neighbor = ContNeighborhood(radius = 0.5), 
            risk = asMSE(), lower = 0, upper = 4)
cniperPoint(P, neighbor = ContNeighborhood(radius = 0.5), 
            risk = asMSE(), lower = 4, upper = 8)

Compare - Plots

Description

Plots 2-4 influence curves to the same model.

Details

S4-Method comparePlot for signature IC,IC has been enhanced compared to its original definition in RobAStBase so that if argument MBRB is NA, it is filled automatically by a call to optIC which computes the MBR-IC on the fly. To this end, there is an additional argument n.MBR defaulting to 10000 to determine the number of evaluation points.

Examples

## all (interesting) examples to this function need
## more time than 5 seconds;
## you can find them in 
## system.file("scripts", "examples_taking_longer.R", 
##              package="ROptEst")

Methods for Function get.asGRisk.fct in Package ‘ROptEst’

Description

get.asGRisk.fct-methods to produce a function in r,s,b for computing a particular asGRisk

Usage

get.asGRisk.fct(Risk)
## S4 method for signature 'asMSE'
get.asGRisk.fct(Risk)     
## S4 method for signature 'asL1'
get.asGRisk.fct(Risk)     
## S4 method for signature 'asL4'
get.asGRisk.fct(Risk)     

Arguments

Details

get.asGRisk.fct is used internally in functions getAsRisk and getReq.

Value

Methods

get.asGRisk.fct

signature(Risk = "asMSE"): method for asymptotic mean squared error.

get.asGRisk.fct

signature(Risk = "asL1"): method for asymptotic mean absolute error.

get.asGRisk.fct

signature(Risk = "asL4"): method for asymptotic mean power 4 error.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

Generic Function for Computation of Asymptotic Risks

Description

Generic function for the computation of asymptotic risks. This function is rarely called directly. It is used by other functions.

Usage

getAsRisk(risk, L2deriv, neighbor, biastype, ...)

## S4 method for signature 'asMSE,UnivariateDistribution,Neighborhood,ANY'
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand, trafo, ...)

## S4 method for signature 'asL1,UnivariateDistribution,Neighborhood,ANY'
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand, trafo, ...)

## S4 method for signature 'asL4,UnivariateDistribution,Neighborhood,ANY'
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand, trafo, ...)

## S4 method for signature 'asMSE,EuclRandVariable,Neighborhood,ANY'
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand, trafo, ...)

## S4 method for signature 'asBias,UnivariateDistribution,ContNeighborhood,ANY'
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand = NULL, trafo, ...)

## S4 method for signature 
## 'asBias,UnivariateDistribution,ContNeighborhood,onesidedBias'
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand = NULL, trafo, ...)

## S4 method for signature 
## 'asBias,UnivariateDistribution,ContNeighborhood,asymmetricBias'
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand = NULL, trafo, ...)

## S4 method for signature 
## 'asBias,UnivariateDistribution,TotalVarNeighborhood,ANY'
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand = NULL, trafo, ...)

## S4 method for signature 'asBias,RealRandVariable,ContNeighborhood,ANY'
getAsRisk(
    risk,L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand = NULL, Distr, DistrSymm, L2derivSymm,
    L2derivDistrSymm, Finfo, trafo, z.start, A.start, maxiter, tol,
    warn, verbose = NULL, ...)
## S4 method for signature 'asBias,RealRandVariable,TotalVarNeighborhood,ANY'
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, 
    clip = NULL, cent = NULL, stand = NULL, Distr, DistrSymm, L2derivSymm,
    L2derivDistrSymm, Finfo, trafo, z.start, A.start, maxiter, tol,
    warn, verbose = NULL, ...)

## S4 method for signature 'asCov,UnivariateDistribution,ContNeighborhood,ANY'
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo = NULL, ...)

## S4 method for signature 
## 'asCov,UnivariateDistribution,TotalVarNeighborhood,ANY'
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo = NULL, ...)

## S4 method for signature 'asCov,RealRandVariable,ContNeighborhood,ANY'
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent, stand,
    Distr, trafo = NULL, V.comp =  matrix(TRUE, ncol = nrow(stand),
    nrow = nrow(stand)), w, ...)

## S4 method for signature 
## 'trAsCov,UnivariateDistribution,UncondNeighborhood,ANY'
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo = NULL, ...)

## S4 method for signature 'trAsCov,RealRandVariable,ContNeighborhood,ANY'
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype, clip, cent, stand, Distr,
    trafo = NULL,  V.comp =  matrix(TRUE, ncol = nrow(stand),
    nrow = nrow(stand)), w, ...)
  
## S4 method for signature 
## 'asAnscombe,UnivariateDistribution,UncondNeighborhood,ANY'
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo = NULL, FI, ...)

## S4 method for signature 'asAnscombe,RealRandVariable,ContNeighborhood,ANY'
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype, clip, cent, stand, Distr, trafo = NULL, 
    V.comp =  matrix(TRUE, ncol = nrow(stand), nrow = nrow(stand)),
    FI, w, ...)
  

## S4 method for signature 
## 'asUnOvShoot,UnivariateDistribution,UncondNeighborhood,ANY'
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo, ...)

## S4 method for signature 
## 'asSemivar,UnivariateDistribution,Neighborhood,onesidedBias'
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo, ...)

Arguments

Details

This function is rarely called directly. It is used by other functions/methods.

Value

The asymptotic risk is computed.

Methods

risk = "asMSE", L2deriv = "UnivariateDistribution", neighbor = "Neighborhood", biastype = "ANY":

computes asymptotic mean square error in methods for function getInfRobIC.

risk = "asL1", L2deriv = "UnivariateDistribution", neighbor = "Neighborhood", biastype = "ANY":

computes asymptotic mean absolute error in methods for function getInfRobIC.

risk = "asL4", L2deriv = "UnivariateDistribution", neighbor = "Neighborhood", biastype = "ANY":

computes asymptotic mean power 4 error in methods for function getInfRobIC.

risk = "asMSE", L2deriv = "EuclRandVariable", neighbor = "Neighborhood", biastype = "ANY":

computes asymptotic mean square error in methods for function getInfRobIC.

risk = "asBias", L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "ANY":

computes standardized asymptotic bias in methods for function getInfRobIC.

risk = "asBias", L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "onesidedBias":

computes standardized asymptotic bias in methods for function getInfRobIC.

risk = "asBias", L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "asymmetricBias":

computes standardized asymptotic bias in methods for function getInfRobIC.

risk = "asBias", L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood", biastype = "ANY":

computes standardized asymptotic bias in methods for function getInfRobIC.

risk = "asBias", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood", biastype = "ANY":

computes standardized asymptotic bias in methods for function getInfRobIC.

risk = "asCov", L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "ANY":

computes asymptotic covariance in methods for function getInfRobIC.

risk = "asCov", L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood", biastype = "ANY":

computes asymptotic covariance in methods for function getInfRobIC.

risk = "asCov", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood", biastype = "ANY":

computes asymptotic covariance in methods for function getInfRobIC.

risk = "trAsCov", L2deriv = "UnivariateDistribution", neighbor = "UncondNeighborhood", biastype = "ANY":

computes trace of asymptotic covariance in methods for function getInfRobIC.

risk = "trAsCov", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood", biastype = "ANY":

computes trace of asymptotic covariance in methods for function getInfRobIC.

risk = "asAnscombe", L2deriv = "UnivariateDistribution", neighbor = "UncondNeighborhood", biastype = "ANY":

computes the ARE in the ideal model in methods for function getInfRobIC.

risk = "asAnscombe", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood", biastype = "ANY":

computes the ARE in the ideal model in methods for function getInfRobIC.

risk = "asUnOvShoot", L2deriv = "UnivariateDistribution", neighbor = "UncondNeighborhood", biastype = "ANY":

computes asymptotic under-/overshoot risk in methods for function getInfRobIC.

risk = "asSemivar", L2deriv = "UnivariateDistribution", neighbor = "Neighborhood", biastype = "onesidedBias":

computes asymptotic semivariance in methods for function getInfRobIC.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

M. Kohl, P. Ruckdeschel, and H. Rieder (2010). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Statistical Methods and Applications 19(3): 333-354. doi:10.1007/s10260-010-0133-0.

H. Rieder (1994): Robust Asymptotic Statistics. Springer. doi:10.1007/978-1-4684-0624-5

P. Ruckdeschel (2005). Optimally One-Sided Bounded Influence Curves. Mathematical Methods of Statistics 14(1), 105-131.

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

See Also

asRisk-class

Generic function for the computation of the asymptotic bias for an IC

Description

Generic function for the computation of the asymptotic bias for an IC.

Usage

getBiasIC(IC, neighbor, ...)

## S4 method for signature 'HampIC,UncondNeighborhood'
getBiasIC(IC, neighbor, L2Fam, ...)

Arguments

Details

This function is rarely called directly. It is used by other functions/methods.

Value

The bias of the IC is computed.

Methods

IC = "HampIC", neighbor = "UncondNeighborhood"

reads off the as. bias from the risks-slot of the IC.

IC = "TotalVarIC", neighbor = "UncondNeighborhood"

reads off the as. bias from the risks-slot of the IC, resp. if this is NULL from the corresponding Lagrange Multipliers.

Note

This generic function is still under construction.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

Ruckdeschel, P. and Kohl, M. (2005) Computation of the Finite Sample Bias of M-estimators on Neighborhoods.

See Also

getRiskIC-methods, InfRobModel-class

Generic Function for the Computation of the Optimal Clipping Bound

Description

Generic function for the computation of the optimal clipping bound in case of robust models with fixed neighborhoods. This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

getFixClip(clip, Distr, risk, neighbor,  ...)

## S4 method for signature 'numeric,Norm,fiUnOvShoot,ContNeighborhood'
getFixClip(clip, Distr, risk, neighbor)

## S4 method for signature 'numeric,Norm,fiUnOvShoot,TotalVarNeighborhood'
getFixClip(clip, Distr, risk, neighbor)

Arguments

Value

The optimal clipping bound is computed.

Methods

clip = "numeric", Distr = "Norm", risk = "fiUnOvShoot", neighbor = "ContNeighborhood"

optimal clipping bound for finite-sample under-/overshoot risk.

clip = "numeric", Distr = "Norm", risk = "fiUnOvShoot", neighbor = "TotalVarNeighborhood"

optimal clipping bound for finite-sample under-/overshoot risk.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

ContIC-class, TotalVarIC-class

Generic Function for the Computation of Optimally Robust ICs

Description

Generic function for the computation of optimally robust ICs in case of robust models with fixed neighborhoods. This function is rarely called directly.

Usage

getFixRobIC(Distr, risk, neighbor, ...)

## S4 method for signature 'Norm,fiUnOvShoot,UncondNeighborhood'
getFixRobIC(Distr, risk, neighbor, 
          sampleSize, upper, lower, maxiter, tol, warn, Algo, cont)

Arguments

Details

Computation of the optimally robust IC in sense of Huber (1968) which is also treated in Kohl (2005). The Algorithm used to compute the exact finite sample risk is introduced and explained in Kohl (2005). It is based on FFT.

Value

The optimally robust IC is computed.

Methods

Distr = "Norm", risk = "fiUnOvShoot", neighbor = "UncondNeighborhood"

computes the optimally robust influence curve for one-dimensional normal location and finite-sample under-/overshoot risk.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106-115.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

FixRobModel-class

Generic Function for the Computation of Inefficiency Differences

Description

Generic function for the computation of inefficiency differencies. This function is rarely called directly. It is used to compute the radius minimax IC and the least favorable radius.

Usage

getIneffDiff(radius, L2Fam, neighbor, risk, ...)

## S4 method for signature 'numeric,L2ParamFamily,UncondNeighborhood,asMSE'
getIneffDiff(
          radius, L2Fam, neighbor, risk, loRad, upRad, loRisk, upRisk, 
          z.start = NULL, A.start = NULL, upper.b = NULL, lower.b = NULL,
          OptOrIter = "iterate", MaxIter, eps, warn, loNorm = NULL, upNorm = NULL,
          verbose = NULL, ..., withRetIneff = FALSE)

Arguments

Value

The inefficieny difference between the left and the right margin of a given radius interval is computed.

Methods

radius = "numeric", L2Fam = "L2ParamFamily", neighbor = "UncondNeighborhood", risk = "asMSE":

computes difference of asymptotic MSE–inefficiency for the boundaries of a given radius interval.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

H. Rieder, M. Kohl, and P. Ruckdeschel (2008). The Costs of not Knowing the Radius. Statistical Methods and Applications, 17(1) 13-40. doi:10.1007/s10260-007-0047-7.

H. Rieder, M. Kohl, and P. Ruckdeschel (2001). The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under doi:10.18452/3638.

P. Ruckdeschel (2005). Optimally One-Sided Bounded Influence Curves. Mathematical Methods of Statistics 14(1), 105-131.

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

See Also

radiusMinimaxIC, leastFavorableRadius

Generic Function for the Computation of the Optimal Centering Constant/Lower Clipping Bound

Description

Generic function for the computation of the optimal centering constant (contamination neighborhoods) respectively, of the optimal lower clipping bound (total variation neighborhood). This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

getInfCent(L2deriv, neighbor, biastype, ...)

## S4 method for signature 'UnivariateDistribution,ContNeighborhood,BiasType'
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

## S4 method for signature 
## 'UnivariateDistribution,TotalVarNeighborhood,BiasType'
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

## S4 method for signature 'RealRandVariable,ContNeighborhood,BiasType'
getInfCent(L2deriv,
     neighbor, biastype, Distr, z.comp, w, tol.z = .Machine$double.eps^.5, ...)

## S4 method for signature 'RealRandVariable,TotalVarNeighborhood,BiasType'
getInfCent(L2deriv,
     neighbor, biastype, Distr, z.comp, w, tol.z = .Machine$double.eps^.5,...)

## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,onesidedBias'
getInfCent(L2deriv,
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,asymmetricBias'
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

Arguments

Value

The optimal centering constant is computed.

Methods

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "BiasType"

computation of optimal centering constant for symmetric bias.

L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood", biastype = "BiasType"

computation of optimal lower clipping bound for symmetric bias.

L2deriv = "RealRandVariable", neighbor = "TotalVarNeighborhood", biastype = "BiasType"

computation of optimal centering constant for symmetric bias.

L2deriv = "RealRandVariable", neighbor = "ContNeighborhood", biastype = "BiasType"

computation of optimal centering constant for symmetric bias.

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "onesidedBias"

computation of optimal centering constant for onesided bias.

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "asymmetricBias"

computation of optimal centering constant for asymmetric bias.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

ContIC-class, TotalVarIC-class

Generic Function for the Computation of the Optimal Clipping Bound

Description

Generic function for the computation of the optimal clipping bound in case of infinitesimal robust models. This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

getInfClip(clip, L2deriv, risk, neighbor, ...)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asMSE,ContNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asMSE,TotalVarNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL1,ContNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL1,TotalVarNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL4,ContNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL4,TotalVarNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 'numeric,EuclRandVariable,asMSE,UncondNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, Distr, stand, cent, trafo, ...)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asUnOvShoot,UncondNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asSemivar,ContNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo,...)

Arguments

Value

The optimal clipping bound is computed.

Methods

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "EuclRandVariable", risk = "asMSE", neighbor = "UncondNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean absolute error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean absolute error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean power 4 error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean power 4 error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "UncondNeighborhood"

optimal clipping bound for asymtotic under-/overshoot risk.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asSemivar", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic semivariance.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

ContIC-class, TotalVarIC-class

Generic Function for the Computation of the Optimal Clipping Bound

Description

Generic function for the computation of the optimal clipping bound. This function is rarely called directly. It is called by getInfClip to compute optimally robust ICs.

Usage

getInfGamma(L2deriv, risk, neighbor, biastype, ...)

## S4 method for signature 
## 'UnivariateDistribution,asGRisk,ContNeighborhood,BiasType'
getInfGamma(L2deriv, 
     risk, neighbor, biastype, cent, clip)

## S4 method for signature 
## 'UnivariateDistribution,asGRisk,TotalVarNeighborhood,BiasType'
getInfGamma(L2deriv, 
     risk, neighbor, biastype, cent, clip)

## S4 method for signature 'RealRandVariable,asMSE,ContNeighborhood,BiasType'
getInfGamma(L2deriv, 
     risk, neighbor, biastype, Distr, stand, cent, clip, power = 1L, ...)

## S4 method for signature 
## 'RealRandVariable,asMSE,TotalVarNeighborhood,BiasType'
getInfGamma(L2deriv,
     risk, neighbor, biastype, Distr, stand, cent, clip, power = 1L, ...)

## S4 method for signature 
## 'UnivariateDistribution,asUnOvShoot,ContNeighborhood,BiasType'
getInfGamma(L2deriv,
     risk, neighbor, biastype, cent, clip)

## S4 method for signature 
## 'UnivariateDistribution,asMSE,ContNeighborhood,onesidedBias'
getInfGamma(L2deriv, 
     risk, neighbor, biastype, cent, clip)

## S4 method for signature 
## 'UnivariateDistribution,asMSE,ContNeighborhood,asymmetricBias'
getInfGamma(L2deriv, 
    risk, neighbor, biastype, cent, clip)

Arguments

Details

The function is used in case of asymptotic G-risks; confer Ruckdeschel and Rieder (2004).

Value

The optimal clipping height is computed. More specifically, the optimal clipping height b is determined in a zero search of a certain function \gamma, where the respective getInf-method will return the value of \gamma(b). The actual function \gamma varies according to whether the parameter is one dimensional or higher dimensional, according to the risk, according to the neighborhood, and according to the bias type, which leads to the different methods.

Methods

L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "ContNeighborhood", biastype = "BiasType"

used by getInfClip for symmetric bias.

L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "TotalVarNeighborhood", biastype = "BiasType"

used by getInfClip for symmetric bias.

L2deriv = "RealRandVariable", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "BiasType"

used by getInfClip for symmetric bias.

L2deriv = "RealRandVariable", risk = "asMSE", neighbor = "TotalVarNeighborhood", biastype = "BiasType"

used by getInfClip for symmetric bias.

L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "ContNeighborhood", biastype = "BiasType"

used by getInfClip for symmetric bias.

L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "onesidedBias"

used by getInfClip for onesided bias.

L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "asymmetricBias"

used by getInfClip for asymmetric bias.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asGRisk-class, asMSE-class, asUnOvShoot-class, ContIC-class, TotalVarIC-class

Functions to determine Lagrange multipliers

Description

Functions to determine Lagrange multipliers A and a in a Hampel problem or in a(n) (inner) loop in a MSE problem; can be done either by optimization or by fixed point iteration. These functions are rarely called directly.

Usage

getLagrangeMultByIter(b, L2deriv, risk, trafo,
                      neighbor, biastype, normtype, Distr,
                      a.start, z.start, A.start, w.start, std, z.comp,
                      A.comp, maxiter, tol, verbose = NULL,
                      warnit = TRUE, ...)
getLagrangeMultByOptim(b, L2deriv, risk, FI, trafo,
                      neighbor, biastype, normtype, Distr,
                      a.start, z.start, A.start, w.start,  std, z.comp,
                      A.comp, maxiter, tol, verbose = NULL, ...)

Arguments

Value

a list with items

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106-115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22: 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

InfRobModel-class

Generic Function for the Computation of the Optimal Radius for Given Clipping Bound

Description

The usual robust optimality problem for given asGRisk searches the optimal clipping height b of a Hampel-type IC to given radius of the neighborhood. Instead, again for given asGRisk and for given Hampel-Type IC with given clipping height b we may determine the radius of the neighborhood for which it is optimal in the sense of the first sentence. This radius is determined by getInfRad. This function is rarely called directly. It is used withing getRadius.

Usage

getInfRad(clip, L2deriv, risk, neighbor, ...)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asMSE,ContNeighborhood'
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asMSE,TotalVarNeighborhood'
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL1,ContNeighborhood'
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL1,TotalVarNeighborhood'
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL4,ContNeighborhood'
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL4,TotalVarNeighborhood'
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 'numeric,EuclRandVariable,asMSE,UncondNeighborhood'
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, Distr, stand, cent, trafo, ...)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asUnOvShoot,UncondNeighborhood'
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asSemivar,ContNeighborhood'
getInfRad(
          clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

Arguments

Value

The optimal clipping bound is computed.

Methods

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "EuclRandVariable", risk = "asMSE", neighbor = "UncondNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean absolute error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean absolute error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean power 4 error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean power 4 error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "UncondNeighborhood"

optimal clipping bound for asymtotic under-/overshoot risk.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asSemivar", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic semivariance.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

ContIC-class, TotalVarIC-class

Generic Function for the Computation of Optimally Robust ICs

Description

Generic function for the computation of optimally robust ICs in case of infinitesimal robust models. This function is rarely called directly.

Usage

getInfRobIC(L2deriv, risk, neighbor, ...)

## S4 method for signature 'UnivariateDistribution,asCov,ContNeighborhood'
getInfRobIC(L2deriv,
                       risk, neighbor, Finfo, trafo, verbose = NULL)

## S4 method for signature 'UnivariateDistribution,asCov,TotalVarNeighborhood'
getInfRobIC(L2deriv,
                       risk, neighbor, Finfo, trafo, verbose = NULL)

## S4 method for signature 'RealRandVariable,asCov,UncondNeighborhood'
getInfRobIC(L2deriv, risk,
                       neighbor, Distr, Finfo, trafo, QuadForm = diag(nrow(trafo)),
                       verbose = NULL)

## S4 method for signature 'UnivariateDistribution,asBias,UncondNeighborhood'
getInfRobIC(L2deriv,
                       risk, neighbor, symm, trafo, maxiter, tol, warn, Finfo,
                       verbose = NULL, ...)

## S4 method for signature 'RealRandVariable,asBias,UncondNeighborhood'
getInfRobIC(L2deriv, risk,
                       neighbor, Distr, DistrSymm, L2derivSymm,
                       L2derivDistrSymm, z.start, A.start, Finfo, trafo,
                       maxiter, tol, warn, verbose = NULL, ...)

## S4 method for signature 'UnivariateDistribution,asHampel,UncondNeighborhood'
getInfRobIC(L2deriv,
                       risk, neighbor, symm, Finfo, trafo, upper = NULL,
                       lower=NULL, maxiter, tol, warn, noLow = FALSE,
                       verbose = NULL, checkBounds = TRUE, ...)

## S4 method for signature 'RealRandVariable,asHampel,UncondNeighborhood'
getInfRobIC(L2deriv, risk,
                       neighbor, Distr, DistrSymm, L2derivSymm,
                       L2derivDistrSymm, Finfo, trafo, onesetLM = FALSE,
                       z.start, A.start, upper = NULL, lower=NULL,
                       OptOrIter = "iterate", maxiter, tol, warn,
                       verbose = NULL, checkBounds = TRUE, ...,
                       .withEvalAsVar = TRUE)

## S4 method for signature 
## 'UnivariateDistribution,asAnscombe,UncondNeighborhood'
getInfRobIC(
                       L2deriv, risk, neighbor, symm, Finfo, trafo, upper = NULL,
                       lower=NULL, maxiter, tol, warn, noLow = FALSE,
                       verbose = NULL, checkBounds = TRUE, ...)

## S4 method for signature 'RealRandVariable,asAnscombe,UncondNeighborhood'
getInfRobIC(L2deriv, 
                       risk, neighbor, Distr, DistrSymm, L2derivSymm,
                       L2derivDistrSymm, Finfo, trafo, onesetLM = FALSE,
                       z.start, A.start, upper = NULL, lower=NULL,
                       OptOrIter = "iterate", maxiter, tol, warn,
                       verbose = NULL, checkBounds = TRUE, ...)

## S4 method for signature 'UnivariateDistribution,asGRisk,UncondNeighborhood'
getInfRobIC(L2deriv,
                       risk, neighbor, symm, Finfo, trafo, upper = NULL,
                       lower = NULL, maxiter, tol, warn, noLow = FALSE,
                       verbose = NULL, ...)

## S4 method for signature 'RealRandVariable,asGRisk,UncondNeighborhood'
getInfRobIC(L2deriv, risk,
                       neighbor,  Distr, DistrSymm, L2derivSymm,
                       L2derivDistrSymm, Finfo, trafo, onesetLM = FALSE, z.start,
                       A.start, upper = NULL, lower = NULL, OptOrIter = "iterate",
                       maxiter, tol, warn, verbose = NULL, withPICcheck = TRUE,
                       ..., .withEvalAsVar = TRUE)

## S4 method for signature 
## 'UnivariateDistribution,asUnOvShoot,UncondNeighborhood'
getInfRobIC(
                       L2deriv, risk, neighbor, symm, Finfo, trafo,
                       upper, lower, maxiter, tol, warn, verbose = NULL, ...)

Arguments

Value

The optimally robust IC is computed.

Methods

L2deriv = "UnivariateDistribution", risk = "asCov", neighbor = "ContNeighborhood"

computes the classical optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.

L2deriv = "UnivariateDistribution", risk = "asCov", neighbor = "TotalVarNeighborhood"

computes the classical optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.

L2deriv = "RealRandVariable", risk = "asCov", neighbor = "UncondNeighborhood"

computes the classical optimal influence curve for L2 differentiable parametric families with unknown k-dimensional parameter (k > 1) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a 1\times k transformation trafo matrix.

L2deriv = "UnivariateDistribution", risk = "asBias", neighbor = "UncondNeighborhood"

computes the bias optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.

L2deriv = "RealRandVariable", risk = "asBias", neighbor = "UncondNeighborhood"

computes the bias optimal influence curve for L2 differentiable parametric families with unknown k-dimensional parameter (k > 1) where the underlying distribution is univariate.

L2deriv = "UnivariateDistribution", risk = "asHampel", neighbor = "UncondNeighborhood"

computes the optimally robust influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.

L2deriv = "RealRandVariable", risk = "asHampel", neighbor = "UncondNeighborhood"

computes the optimally robust influence curve for L2 differentiable parametric families with unknown k-dimensional parameter (k > 1) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a 1\times k transformation trafo matrix.

L2deriv = "UnivariateDistribution", risk = "asAnscombe", neighbor = "UncondNeighborhood"

computes the optimally bias-robust influence curve to given ARE in the ideal model for L2 differentiable parametric families with unknown one-dimensional parameter.

L2deriv = "RealRandVariable", risk = "asAnscombe", neighbor = "UncondNeighborhood"

computes the optimally bias-robust influence curve to given ARE in the ideal modelfor L2 differentiable parametric families with unknown k-dimensional parameter (k > 1) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a 1\times k transformation trafo matrix.

L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "UncondNeighborhood"

computes the optimally robust influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.

L2deriv = "RealRandVariable", risk = "asGRisk", neighbor = "UncondNeighborhood"

computes the optimally robust influence curve for L2 differentiable parametric families with unknown k-dimensional parameter (k > 1) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a 1\times k transformation trafo matrix.

L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "UncondNeighborhood"

computes the optimally robust influence curve for one-dimensional L2 differentiable parametric families and asymptotic under-/overshoot risk.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106-115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22: 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

InfRobModel-class

Generic Function for the Computation of the Standardizing Matrix

Description

Generic function for the computation of the standardizing matrix which takes care of the Fisher consistency of the corresponding IC. This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

getInfStand(L2deriv, neighbor, biastype, ...)

## S4 method for signature 'UnivariateDistribution,ContNeighborhood,BiasType'
getInfStand(L2deriv, 
     neighbor, biastype, clip, cent, trafo)

## S4 method for signature 
## 'UnivariateDistribution,TotalVarNeighborhood,BiasType'
getInfStand(L2deriv, 
     neighbor, biastype, clip, cent, trafo)

## S4 method for signature 'RealRandVariable,UncondNeighborhood,BiasType'
getInfStand(L2deriv,
     neighbor, biastype, Distr, A.comp, cent, trafo, w, ...)

## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,onesidedBias'
getInfStand(L2deriv,
     neighbor, biastype, clip, cent, trafo, ...)

## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,asymmetricBias'
getInfStand(L2deriv,
     neighbor, biastype, clip, cent, trafo)

Arguments

Value

The standardizing matrix is computed.

Methods

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "BiasType"

computes standardizing matrix for symmetric bias.

L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood", biastype = "BiasType"

computes standardizing matrix for symmetric bias.

L2deriv = "RealRandVariable", neighbor = "UncondNeighborhood", biastype = "BiasType"

computes standardizing matrix for symmetric bias.

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "onesidedBias"

computes standardizing matrix for onesided bias.

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "asymmetricBias"

computes standardizing matrix for asymmetric bias.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

ContIC-class, TotalVarIC-class

Generic Function for the Computation of the asymptotic Variance of a Hampel type IC

Description

Generic function for the computation of the optimal clipping bound in case of infinitesimal robust models. This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

getInfV(L2deriv, neighbor, biastype, ...)
## S4 method for signature 'UnivariateDistribution,ContNeighborhood,BiasType'
getInfV(L2deriv, 
         neighbor, biastype, clip, cent, stand)
## S4 method for signature 
## 'UnivariateDistribution,TotalVarNeighborhood,BiasType'
getInfV(L2deriv, 
         neighbor, biastype, clip, cent, stand)
## S4 method for signature 'RealRandVariable,ContNeighborhood,BiasType'
getInfV(L2deriv, 
         neighbor, biastype, Distr, V.comp, cent, stand, 
         w, ...)
## S4 method for signature 'RealRandVariable,TotalVarNeighborhood,BiasType'
getInfV(L2deriv,
         neighbor, biastype, Distr, V.comp, cent, stand,
         w, ...)
## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,onesidedBias'
getInfV(L2deriv,
         neighbor, biastype, clip, cent, stand, ...)
## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,asymmetricBias'
getInfV(L2deriv, 
         neighbor, biastype, clip, cent, stand)

Arguments

Value

The asymptotic variance of an ALE to IC of Hampel type is computed.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

ContIC-class, TotalVarIC-class

Calculation of L1 norm of L2derivative

Description

Methods to calculate the L1 norm of the L2derivative in a smooth parametric model.

Usage

getL1normL2deriv(L2deriv, ...)
## S4 method for signature 'UnivariateDistribution'
getL1normL2deriv(L2deriv, 
     cent, ...)

## S4 method for signature 'RealRandVariable'
getL1normL2deriv(L2deriv, 
     cent, stand, Distr, normtype, ...)

Arguments

Value

L1 norm of the L2derivative

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

Examples

##

Calculation of L2 norm of L2derivative

Description

Function to calculate the L2 norm of the L2derivative in a smooth parametric model.

Usage

getL2normL2deriv(aFinfo, cent, ...)

Arguments

Value

L2 norm of the L2derivative

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

Examples

##

getMaxIneff – computation of the maximal inefficiency of an IC

Description

computes the maximal inefficiency of an IC for the radius range [0,Inf).

Usage

getMaxIneff(IC, neighbor, biastype = symmetricBias(), 
                        normtype = NormType(), z.start = NULL, 
                        A.start = NULL, maxiter = 50, 
                        tol = .Machine$double.eps^0.4,
                        warn = TRUE, verbose = NULL, ...)

Arguments

Value

The maximal inefficiency, i.e.; a number in [1,Inf).

Author(s)

Peter Ruckdeschel peter.ruckdeschel@fraunhofer.itwm.de

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

H. Rieder, M. Kohl, and P. Ruckdeschel (2008). The Costs of not Knowing the Radius. Statistical Methods and Applications, 17(1) 13-40. doi:10.1007/s10260-007-0047-7.

H. Rieder, M. Kohl, and P. Ruckdeschel (2001). The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under doi:10.18452/3638.

P. Ruckdeschel (2005). Optimally One-Sided Bounded Influence Curves. Mathematical Methods of Statistics 14(1), 105-131.

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

Examples

N0 <- NormLocationFamily(mean=2, sd=3)
## L_2 family + infinitesimal neighborhood
neighbor <- ContNeighborhood(radius = 0.5)
N0.Rob1 <- InfRobModel(center = N0, neighbor = neighbor)
## OBRE solution (ARE 95%)
N0.ICA <- optIC(model = N0.Rob1, risk = asAnscombe(.95))
## OMSE solution radius 0.5
N0.ICM <- optIC(model=N0.Rob1, risk=asMSE())
## RMX solution 
N0.ICR <- radiusMinimaxIC(L2Fam=N0, neighbor=neighbor,risk=asMSE())

getMaxIneff(N0.ICA,neighbor)
getMaxIneff(N0.ICM,neighbor)
getMaxIneff(N0.ICR,neighbor)

## Don't run to reduce check time on CRAN

N0ls <- NormLocationScaleFamily()
ICsc <- makeIC(list(sin,cos),N0ls)
getMaxIneff(ICsc,neighbor)

Generic Function for the Computation of Functions for Slot modifyIC

Description

These function is used by internal computations and is rarely called directly.

Usage

getModifyIC(L2FamIC, neighbor, risk,...)
## S4 method for signature 'L2ParamFamily,Neighborhood,asRisk'
getModifyIC(L2FamIC,
          neighbor, risk, ...)
## S4 method for signature 'L2LocationFamily,UncondNeighborhood,asGRisk'
getModifyIC(L2FamIC,
          neighbor, risk, ...)
## S4 method for signature 'L2LocationFamily,UncondNeighborhood,fiUnOvShoot'
getModifyIC(L2FamIC,
          neighbor, risk, ...)
## S4 method for signature 'L2ScaleFamily,UncondNeighborhood,asGRisk'
getModifyIC(L2FamIC,
          neighbor, risk, ..., modifyICwarn = NULL)
## S4 method for signature 'L2LocationScaleFamily,UncondNeighborhood,asGRisk'
getModifyIC(L2FamIC,
          neighbor, risk, ..., modifyICwarn = NULL)

scaleUpdateIC(neighbor,...)
## S4 method for signature 'UncondNeighborhood'
scaleUpdateIC(neighbor, sdneu, sdalt, IC)
## S4 method for signature 'ContNeighborhood'
scaleUpdateIC(neighbor, sdneu, sdalt, IC)
## S4 method for signature 'TotalVarNeighborhood'
scaleUpdateIC(neighbor, sdneu, sdalt, IC)

Arguments

Details

This function is used for internal computations. By setting RobAStBaseOption("all.verbose" = TRUE) somewhere globally, the generated function modifyIC will generate calls to optIC with argument verbose=TRUE.

Value

getmodifyIC

Function for slot modifyIC of ICs

scaleUpdateIC

a list to be digested in corresponding methods of getmodifyIC by generateIC

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

optIC, IC-class

Computation of the Optimal Radius for Given Clipping Bound

Description

The usual robust optimality problem for given asGRisk searches the optimal clipping height b of a Hampel-type IC to given radius of the neighborhood. Instead, again for given asGRisk and for given Hampel-Type IC with given clipping height b we may determine the radius of the neighborhood for which it is optimal in the sense of the first sentence.

Usage

getRadius(IC, risk, neighbor, L2Fam)

Arguments

Value

The optimal radius is computed.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

ContIC-class, TotalVarIC-class

Examples

N <- NormLocationFamily(mean=0, sd=1)
nb <- ContNeighborhood(); ri <- asMSE()
radIC <- radiusMinimaxIC(L2Fam=N, neighbor=nb, risk=ri, loRad=0.1, upRad=0.5)
getRadius(radIC, L2Fam=N, neighbor=nb, risk=ri)

## taken from script NormalScaleModel.R in folder scripts
N0 <- NormScaleFamily(mean=0, sd=1)
(N0.IC7 <- radiusMinimaxIC(L2Fam=N0, neighbor=nb, risk=ri, loRad=0, upRad=Inf))
##
getRadius(N0.IC7, risk=asMSE(), neighbor=nb, L2Fam=N0)
getRadius(N0.IC7, risk=asL4(), neighbor=nb, L2Fam=N0)

getReq – computation of the radius interval where IC1 is better than IC2.

Description

(tries to) compute a radius interval where IC1 is better than IC2, respectively the number of (worst-case) outliers interval where IC1 is better than IC2.

Usage

getReq(Risk,neighbor,IC1,IC2,n=1,upper=15, radOrOutl=c("radius","Outlier"), ...)

Arguments

Value

The radius interval (given by its endpoints) where IC1 is better than IC2 according to the risk. In case IC2 is better than IC1 as to both variance and bias, the return value is NA.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@fraunhofer.itwm.de

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Examples

N0 <- NormLocationFamily(mean=2, sd=3)
## L_2 family + infinitesimal neighborhood
neighbor <- ContNeighborhood(radius = 0.5)
N0.Rob1 <- InfRobModel(center = N0, neighbor = neighbor)
## OBRE solution (ARE 95%)
N0.ICA <- optIC(model = N0.Rob1, risk = asAnscombe(.95))
## MSE solution
N0.ICM <- optIC(model=N0.Rob1, risk=asMSE())

getReq(asMSE(),neighbor,N0.ICA,N0.ICM,n=1)
getReq(asMSE(),neighbor,N0.ICA,N0.ICM,n=30)

## Don't test to reduce check time on CRAN

## RMX solution
N0.ICR <- radiusMinimaxIC(L2Fam=N0, neighbor=neighbor,risk=asMSE())

getReq(asL1(),neighbor,N0.ICA,N0.ICM,n=30)
getReq(asL4(),neighbor,N0.ICA,N0.ICM,n=30)
getReq(asMSE(),neighbor,N0.ICA,N0.ICR,n=30)
getReq(asL1(),neighbor,N0.ICA,N0.ICR,n=30)
getReq(asL4(),neighbor,N0.ICA,N0.ICR,n=30)
getReq(asMSE(),neighbor,N0.ICM,N0.ICR,n=30)


### when to use MAD and when Qn 
##  for Qn, see C. Croux, P. Rousseeuw (1993). Alternatives to the Median 
##      Absolute Deviation, JASA 88(424):1273-1283
L2M <- NormScaleFamily()
IC.mad <- makeIC(function(x)sign(abs(x)-qnorm(.75)),L2M)
d.qn <- (2^.5*qnorm(5/8))^-1
IC.qn <- makeIC(function(x) d.qn*(1/4 - pnorm(x+1/d.qn) + pnorm(x-1/d.qn)), L2M)
getReq(asMSE(), neighbor, IC.mad, IC.qn)
getReq(asMSE(), neighbor, IC.mad, IC.qn, radOrOutl = "Outlier", n = 30)
# => MAD is better once r > 0.5144 (i.e. for more than 2 outliers for n = 30)

Methods for Function getRiskFctBV in Package ‘ROptEst’

Description

getRiskFctBV for a given object of S4 class asGRisk returns a function in bias and variance to compute the asymptotic risk.

Methods

getRiskFctBV

signature(risk = "asL1", biastype = "ANY"): returns a function with arguments bias and variance to compute the asymptotic absolute (L1) error for a given ALE at a situation where it has bias bias (including the radius!) and variance variance.

getRiskFctBV

signature(risk = "asL4", biastype = "ANY"): returns a function with arguments bias and variance to compute the asymptotic L4 error for a given ALE at a situation where it has bias bias (including the radius!) and variance variance.

Examples

myrisk <- asMSE()
getRiskFctBV(myrisk)

Generic function for the computation of a risk for an IC

Description

Generic function for the computation of a risk for an IC.

Usage

getRiskIC(IC, risk, neighbor, L2Fam, ...)

## S4 method for signature 'HampIC,asCov,missing,missing'
getRiskIC(IC, risk, withCheck= TRUE, ...)

## S4 method for signature 'HampIC,asCov,missing,L2ParamFamily'
getRiskIC(IC, risk, L2Fam, withCheck= TRUE, ...)
## S4 method for signature 'TotalVarIC,asCov,missing,L2ParamFamily'
getRiskIC(IC, risk, L2Fam, withCheck = TRUE, ...)

Arguments

Details

To make sure that the results are valid, it is recommended to include an additional check of the IC properties of IC using checkIC.

Value

The risk of an IC is computed.

Methods

IC = "HampIC", risk = "asCov", neighbor = "missing", L2Fam = "missing"

asymptotic covariance of IC read off from corresp. Risks slot.

IC = "HampIC", risk = "asCov", neighbor = "missing", L2Fam = "L2ParamFamily"

asymptotic covariance of IC under L2Fam read off from corresp. Risks slot.

IC = "TotalVarIC", risk = "asCov", neighbor = "missing", L2Fam = "L2ParamFamily"

asymptotic covariance of IC read off from corresp. Risks slot, resp. if this is NULL calculates it via getInfV.

Note

This generic function is still under construction.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

Ruckdeschel, P. and Kohl, M. (2005) Computation of the Finite Sample Risk of M-estimators on Neighborhoods.

See Also

getRiskIC, InfRobModel-class

Examples

B <- BinomFamily(size = 25, prob = 0.25)

## classical optimal IC
IC0 <- optIC(model = B, risk = asCov())
getRiskIC(IC0, asCov())

Methods for Function getStartIC in Package ‘ROptEst’

Description

getStartIC computes the optimally-robust IC to be used as argument ICstart in kStepEstimator.

Usage

getStartIC(model, risk, ...)
## S4 method for signature 'ANY,ANY'
getStartIC(model, risk, ...)
## S4 method for signature 'L2ParamFamily,asGRisk'
getStartIC(model, risk, ...,
                      withEvalAsVar = TRUE, withMakeIC = FALSE, ..debug=FALSE,
                      modifyICwarn = NULL, diagnostic = FALSE)
## S4 method for signature 'L2ParamFamily,asBias'
getStartIC(model, risk, ..., withMakeIC = FALSE,
        ..debug=FALSE, modifyICwarn = NULL, diagnostic = FALSE)
## S4 method for signature 'L2ParamFamily,asCov'
getStartIC(model, risk, ..., withMakeIC = FALSE,
    ..debug=FALSE)
## S4 method for signature 'L2ParamFamily,trAsCov'
getStartIC(model, risk, ..., withMakeIC = FALSE,
    ..debug=FALSE)
## S4 method for signature 'L2ParamFamily,asAnscombe'
getStartIC(model, risk, ...,
                      withEvalAsVar = TRUE, withMakeIC = FALSE, ..debug=FALSE,
                      modifyICwarn = NULL, diagnostic = FALSE)
## S4 method for signature 'L2LocationFamily,interpolRisk'
getStartIC(model, risk, ...)
## S4 method for signature 'L2ScaleFamily,interpolRisk'
getStartIC(model, risk, ...)
## S4 method for signature 'L2LocationScaleFamily,interpolRisk'
getStartIC(model, risk, ...)

Arguments

Details

getStartIC is used internally in functions robest and roptest to compute the optimally robust influence function according to the arguments given to them.

Value

An IC of type HampIC.

Methods

getStartIC

signature(model = "ANY", risk = "ANY"): issue that this is not yet implemented.

getStartIC

signature(model = "L2ParamFamily", risk = "asGRisk"): depending on the values of argument eps (to be passed on through the ... argument) computes the optimally robust influence function on the fly via calls to optIC or radiusMinimaxIC.

getStartIC

signature(model = "L2ParamFamily", risk = "asBias"): computes the most-bias-robust influence function on the fly via calls to optIC.

getStartIC

signature(model = "L2ParamFamily", risk = "asCov"): computes the classically optimal influence function on the fly via calls to optIC.

getStartIC

signature(model = "L2ParamFamily", risk = "trAsCov"): computes the classically optimal influence function on the fly via calls to optIC.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

See Also

robest,optIC, radiusMinimaxIC

Input generating functions for function 'robest'

Description

Generating functions to generate structured input for function robest.

Usage

genkStepCtrl(useLast = getRobAStBaseOption("kStepUseLast"),
                    withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
                    IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
                    withICList = getRobAStBaseOption("withICList"),
                    withPICList = getRobAStBaseOption("withPICList"),
                    scalename = "scale", withLogScale = TRUE,
                    withEvalAsVar = NULL, withMakeIC = FALSE,
                    E.argList = NULL)
genstartCtrl(initial.est = NULL, initial.est.ArgList = NULL,
                        startPar = NULL, distance = CvMDist, withMDE = NULL,
                        E.argList = NULL)
gennbCtrl(neighbor = ContNeighborhood(), eps, eps.lower, eps.upper)
genstartICCtrl(withMakeIC = FALSE, withEvalAsVar = NULL, modifyICwarn = NULL,
               E.argList = NULL)

Arguments

Details

All these functions bundle their respective input to (reusable) lists which can be used as arguments in function robest. For details, see this function.

Value

A list of arguments to be (re-)used as (structured) input for function robest; more specifically, all arguments of the respective function are bundled into a list, where arguments not explicitly specified in the call are filled with corresponding defaults as given in the usage section of this help file.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

See Also

roblox, L2ParamFamily-class UncondNeighborhood-class, RiskType-class

Examples

genkStepCtrl()
genstartICCtrl()
genstartCtrl()
gennbCtrl()

Internal helper functions for generating interpolation grids for speed up in package ROptEst

Description

These functions are used internally to generate interpolation grids, for Lagrange multipliers or LDEstimators in package RobExtremes, to be stored in the respective ‘sysdata.rda’ file.

Usage

.RMXE.th(th, PFam, modifyfct, loRad = 0, upRad = Inf, z.start = NULL,
             A.start = NULL, upper = NULL, lower = NULL,
             OptOrIter = "iterate", maxiter = 50,
             tol = .Machine$double.eps^0.4, loRad0 = 1e-3, ...)
.MBRE.th(th, PFam, modifyfct,
             z.start = NULL, A.start = NULL, upper = 1e4,
             lower = 1e-4, OptOrIter = "iterate",
             maxiter = 50, tol = .Machine$double.eps^0.4, ...)
.OMSE.th(th, PFam, modifyfct, radius = 0.5,
             z.start = NULL, A.start = NULL, upper = 1e4,
             lower = 1e-4, OptOrIter = "iterate",
             maxiter = 50, tol = .Machine$double.eps^0.4, ...)

.getLMGrid(thGrid, PFam, optFct = .RMXE.th, modifyfct, radius = 0.5,
           GridFileName = "LMGrid.Rdata", withPrint = FALSE,
           upper = 1e4, lower = 1e-4, OptOrIter = "iterate",
           maxiter = 50, tol = .Machine$double.eps^0.4,
           loRad = 0, upRad = Inf, loRad0 = 1e-3,
           loRad.s = 0.2, upRad.s = 1, withStartLM = TRUE, len = 13)


.saveGridToCSV(Grid, toFileCSV, namPFam, nameInSysdata)

.readGridFromCSV(fromFileCSV)

.generateInterpGrid(thGrid, PFam, toFileCSV = "temp.csv",
            getFun = .getLMGrid, ..., modifyfct, nameInSysdata,
            GridFileName, withPrint = TRUE, len = 13)

Arguments

Details

.MBRE.th computes the Lagrange multipliers for the MBRE estimator, .OMSE.th for the OMSE estimator at radius radius, and .RMXE.th the RMXE estimator.

.getLMGrid in a large loop computes the Lagrange multipliers for optimally robust IFs for each element of a given grid.

.saveGridToCSV saves a given grid to a csv file, and in addition, in a file with same name but with file extension ".txt" writes the parametric family and the grid name.

.readGridFromCSV reads in a grid from a csv file together with the information given in the corresponding ".txt" file.

.generateInterpGrid by means of calls to function-argument getFun (e.g. getLMGrid computes the grid, if desired smoothes it, and then saves it to .csv.

Value

Note

These functions are only meant for the developers of package ROptEst (or respective packages). They can be used to speed up things by interpolation. Our use case is a speed up for further scale-shape families (or enhance existing speed-ups) such that the respective grids are stored in a ‘sysdata.rda’ file of an external package RobAStRda —see mail exchange P.Ruckdeschel - U.Ligges on R-devel— https://stat.ethz.ch/pipermail/r-devel/2013-February/065794.html. Special attention has to be paid for R-versions pre and post R-2.16 which is why we use .versionSuff.

Internal / Helper function of package ROptEst for MBRE calculation

Description

This function computes the coordinatewise min and max of an IC numerically.

Usage

.getExtremeCoordIC(IC, D, indi, n = 10000)

Arguments

Value

a matrix with length(indi) rows and 2 columns min and max: the coordinate-wise min and max of the IC.

Internal / Helper functions of package ROptEst

Description

These functions are used internally by package ROptEst.

Usage

### helper function to check whether given b is in (bmin, bmax)
###        if not returns corresponding upper / lower case solution

.checkUpLow(L2deriv, b, risk, neighbor, biastype, normtype,
                        Distr, Finfo, DistrSymm, L2derivSymm,
                        L2derivDistrSymm, z.start, A.start, trafo, maxiter,
                        tol, QuadForm, verbose, nrvalpts, warn, ...)
                        
### helper function to return the upper case solution if r=0
.getUpperSol(L2deriv, radius, risk, neighbor, biastype,
                       normtype, Distr, Finfo, trafo,
                       QuadForm, verbose, warn, ...)

### helper function to return the lower case solution if b-search was not successful
.getLowerSol(L2deriv, risk, neighbor, Distr, DistrSymm,
                         L2derivSymm, L2derivDistrSymm,
                         z.start, A.start, trafo,
                         maxiter, tol, warn, Finfo, QuadForm, verbose, ...)


### helper function to return upper & lower bounds for b for b-search
.getLowUpB(L2deriv, Finfo, Distr, normtype, z, A, radius, iter)

### helper function to check whether (TotalVariation) weight w has already been modified
.isVirginW(w)

### helper function to check whether (intermediate) results give a pIC
.checkPIC(L2deriv, neighbor, Distr, trafo, z, A, w, z.comp, A.comp, ...)

.LowerCaseMultivariate(L2deriv, neighbor, biastype,
             normtype, Distr, Finfo, trafo, z.start = NULL,
             A.start = NULL, z.comp = NULL, A.comp = NULL,
             maxiter, tol, verbose = NULL, ...)

.LowerCaseMultivariateTV(L2deriv, neighbor, biastype,
             normtype, Distr, Finfo, trafo,
             A.start,  maxiter, tol,
             verbose = NULL, ...)

.getSB(IC,neighbor, ...)

Arguments

Details

.checkUpLow checks whether the given clipping height b lies in (b_{\rm\scriptstyle min},b_{\rm\scriptstyle min}); .getUpperSol determines the upper case/classical solution and computes corresponding risks .getLowerSol determines the lower case (minimax bias) solution and computes corresponding risks .getLowUpB determines a search interval for b to given radius r, i.e., lower and upper bounds for (b_{\rm\scriptstyle min},b_{\rm\scriptstyle min}) .isVirginW checks whether the (total variation) weight w in the argument has already been modified since creation (TRUE if not) .checkPIC checks whether (intermediate) results give a pIC .LowerCaseMultivariatefunction determines the Lagrange multipliers for the multivariate lower case solution for convex contamination by solving a corresponding dual problem (Rieder[94],p.199 eq.(18)). .LowerCaseMultivariatefunctionTV determines the Lagrange multipliers for the multivariate lower case solution for total variation in dimension p=1 and k>1 by solving a corresponding dual problem (Rieder[94],p.205 eq.(58)). .getSB computes the bias and (the square root of the trace of) the variance of the IC.

Value

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Internal / Helper functions of package ROptEst for cniper plot functions

Description

These functions are internally used helper function for cniperCont and cniperPointPlot.

Usage

.plotData(data, dots, fun, L2Fam,  IC, jit.fac, jit.tol, plotInfo )
.getFunCnip(IC1,IC2, risk, L2Fam, r, b20=NULL)

Arguments

Details

.plotData takes argument data and plots it into the cniper graph.

.getFunCnip produces a function to compute the risk difference. If argument b20 is not NULL, in the risk difference, for IC2 uses the least favorable contamination situation ('over all real Dirac contamination points'), i.e. leading to a bias of b20. Otherwise it uses the bias obtaine from a contamination in the evaluation point.

Value

Internal / Helper functions of package ROptEst for function robest

Description

These functions are internally used helper functions for robest, in package ROptEst.

Usage

.dynScopeEval(expr)
.constructArg.list(fun,matchCall, onlyFormal=FALSE, debug =FALSE)
.fix.in.defaults(call.list, fun, withEval=TRUE)
.pretreat(x, na.rm = TRUE)
.check.eps(...)
.isOKsteps(steps)
.isOKfsCor(fsCor)

Arguments

Details

.dynScopeEval marches up the stack of calls to evaluate an expression, hence realizes dynamical scoping.

.constructArg.list takes a function fun and the return value of match.call and, as return value, produces a list of arguments where the formal arguments of fun are set to their default values and with extra item esc.

If argument onlyFormals is TRUE and the formals contain ..., the returned list only contains formal arguments of fun, filled with default values from the definition where available, and, in addition, in element esc a list with element one of the original matched call and, as subsequent elements, with the named, evaluated arguments of the matched call which are no formal arguments of fun.

If argument onlyFormals is FALSE or the formals do not contain ..., the returned list again contains formal arguments of fun filled in with defaults where available, but in addition it contains the arguments of the matched calls non matched to formals (in particular those passed on through ...). Then element esc in the returned list with contains element one of the original matched call coerced to list, i.e., the name of the called function.

.fix.in.defaults takes a list of arguments of fun taken from a matched call obtained by match.call from within a call of fun (after coercing to list) and supplements this list by formal arguments of fun which are not yet matched but have default arguments (with exactly these default values). The return value is the prolongated list.

.pretreat, if is.numeric(x) is FALSE, coerces x to a numeric matrix (by a call to data.matrix in case x is a data.frame, respectively, by a call to as.matrix else. If na.rm is TRUE, x is reduced to na.omit(x). The return value is a list of elements x, the possibly modified input x, and completecases, the return value of compeletecases(x).

.check.eps takes its input (possibly empty in part) and returns a list eps with elements sqn, e, lower, and upper. Necessarily the input ... must contain an argument matching to x, and sqn is the square root of either the length of x (if x is a vector) or the number of columns of x (in case dim(x)==2). In case ... contains none of the elements eps, eps.lower, eps.upper, elements lower and upper of the return value are set to 0 and 0.5, respectively. Else, if eps is contained input ... element e of the return list is set to eps, and lower and upper are left empty. Otherwise, element e of the return list is left empty and lower and upper are filled with eps.lower and eps.upper from input ... if available and else with default values 0 and 0.5, respectively.

.isOKsteps checks whether argument steps is a valid argument, i.e., is an integer larger than 0 of length 1 and, accordingly, returns TRUE or FALSE.

.isOKfsCor checks whether argument fsCor is a valid argument, i.e., larger than 0 and of length 1 and, accordingly, returns TRUE or FALSE.

Generic Function for the Computation of Least Favorable Radii

Description

Generic function for the computation of least favorable radii.

Usage

leastFavorableRadius(L2Fam, neighbor, risk, ...)

## S4 method for signature 'L2ParamFamily,UncondNeighborhood,asGRisk'
leastFavorableRadius(
          L2Fam, neighbor, risk, rho, upRad = 1, 
            z.start = NULL, A.start = NULL, upper = 100,
            OptOrIter = "iterate", maxiter = 100,
            tol = .Machine$double.eps^0.4, warn = FALSE, verbose = NULL, ...)

Arguments

Value

The least favorable radius and the corresponding inefficiency are computed.

Methods

L2Fam = "L2ParamFamily", neighbor = "UncondNeighborhood", risk = "asGRisk"

computation of the least favorable radius.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

H. Rieder, M. Kohl, and P. Ruckdeschel (2008). The Costs of not Knowing the Radius. Statistical Methods and Applications, 17(1) 13-40. doi:10.1007/s10260-007-0047-7.

H. Rieder, M. Kohl, and P. Ruckdeschel (2001). The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under doi:10.18452/3638.

P. Ruckdeschel (2005). Optimally One-Sided Bounded Influence Curves. Mathematical Methods of Statistics 14(1), 105-131.

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

See Also

radiusMinimaxIC

Examples

N <- NormLocationFamily(mean=0, sd=1) 
leastFavorableRadius(L2Fam=N, neighbor=ContNeighborhood(),
                     risk=asMSE(), rho=0.5)

Computation of the lower case radius

Description

The lower case radius is computed; confer Subsection 2.1.2 in Kohl (2005) and formula (4.5) in Ruckdeschel (2005).

Usage

lowerCaseRadius(L2Fam, neighbor, risk, biastype, ...)

Arguments

Value

lower case radius

Methods

L2Fam = "L2ParamFamily", neighbor = "ContNeighborhood", risk = "asMSE", biastype = "BiasType"

lower case radius for risk "asMSE" in case of "ContNeighborhood" for symmetric bias.

L2Fam = "L2ParamFamily", neighbor = "TotalVarNeighborhood", risk = "asMSE", biastype = "BiasType"

lower case radius for risk "asMSE" in case of "TotalVarNeighborhood"; (argument biastype is just for signature reasons).

L2Fam = "L2ParamFamily", neighbor = "ContNeighborhood", risk = "asMSE", biastype = "onesidedBias"

lower case radius for risk "asMSE" in case of "ContNeighborhood" for onesided bias.

L2Fam = "L2ParamFamily", neighbor = "ContNeighborhood", risk = "asMSE", biastype = "asymmetricBias"

lower case radius for risk "asMSE" in case of "ContNeighborhood" for asymmetric bias.

L2Fam = "UnivariateDistribution", neighbor = "ContNeighborhood", risk = "asMSE", biastype = "onesidedBias"

used only internally; trick to be able to call lower case radius from within minmax bias solver

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

See Also

L2ParamFamily-class, Neighborhood-class

Examples

lowerCaseRadius(BinomFamily(size = 10), ContNeighborhood(), asMSE())
lowerCaseRadius(BinomFamily(size = 10), TotalVarNeighborhood(), asMSE())

Generic Function for the Computation of Bias-Optimally Robust ICs

Description

Generic function for the computation of bias-optimally robust ICs in case of infinitesimal robust models. This function is rarely called directly.

Usage

minmaxBias(L2deriv, neighbor, biastype, ...)

## S4 method for signature 'UnivariateDistribution,ContNeighborhood,BiasType'
minmaxBias(L2deriv,
     neighbor, biastype, symm, trafo, maxiter, tol, warn, Finfo, verbose = NULL)

## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,asymmetricBias'
minmaxBias(
     L2deriv, neighbor, biastype, symm, trafo, maxiter, tol, warn, Finfo, verbose = NULL)

## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,onesidedBias'
minmaxBias(
     L2deriv, neighbor, biastype, symm, trafo, maxiter, tol, warn, Finfo, verbose = NULL)

## S4 method for signature 
## 'UnivariateDistribution,TotalVarNeighborhood,BiasType'
minmaxBias(
     L2deriv, neighbor, biastype, symm, trafo, maxiter, tol, warn, Finfo, verbose = NULL)

## S4 method for signature 'RealRandVariable,ContNeighborhood,BiasType'
minmaxBias(L2deriv,
     neighbor, biastype, normtype, Distr, z.start, A.start,  z.comp, A.comp,
     Finfo, trafo, maxiter, tol, verbose = NULL, ...)

## S4 method for signature 'RealRandVariable,TotalVarNeighborhood,BiasType'
minmaxBias(L2deriv,
     neighbor, biastype, normtype, Distr, z.start, A.start,  z.comp, A.comp,
     Finfo, trafo, maxiter, tol, verbose = NULL, ...)

Arguments

Value

The bias-optimally robust IC is computed.

Methods

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "BiasType"

computes the bias optimal influence curve for symmetric bias for L2 differentiable parametric families with unknown one-dimensional parameter.

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "asymmetricBias"

computes the bias optimal influence curve for asymmetric bias for L2 differentiable parametric families with unknown one-dimensional parameter.

L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood", biastype = "BiasType"

computes the bias optimal influence curve for symmetric bias for L2 differentiable parametric families with unknown one-dimensional parameter.

L2deriv = "RealRandVariable", neighbor = "ContNeighborhood", biastype = "BiasType"

computes the bias optimal influence curve for symmetric bias for L2 differentiable parametric families with unknown k-dimensional parameter (k > 1) where the underlying distribution is univariate.

L2deriv = "RealRandVariable", neighbor = "TotalNeighborhood", biastype = "BiasType"

computes the bias optimal influence curve for symmetric bias for L2 differentiable parametric families in a setting where we are interested in a p=1 dimensional aspect of an unknown k-dimensional parameter (k > 1) where the underlying distribution is univariate.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

InfRobModel-class

Generic function for the computation of optimally robust ICs

Description

Generic function for the computation of optimally robust ICs.

Usage

optIC(model, risk, ...)

## S4 method for signature 'InfRobModel,asRisk'
optIC(model, risk, z.start = NULL, A.start = NULL,
                                     upper = 1e4, lower = 1e-4,
                                     OptOrIter = "iterate", maxiter = 50,
                                     tol = .Machine$double.eps^0.4, warn = TRUE, 
                                     noLow = FALSE, verbose = NULL, ...,
                                     .withEvalAsVar = TRUE, withMakeIC = FALSE,
                                     returnNAifProblem = FALSE, modifyICwarn = NULL)

## S4 method for signature 'InfRobModel,asUnOvShoot'
optIC(model, risk, upper = 1e4,
                                          lower = 1e-4, maxiter = 50,
                                          tol = .Machine$double.eps^0.4,
                                          withMakeIC = FALSE, warn = TRUE,
                                          verbose = NULL, modifyICwarn = NULL, ...)

## S4 method for signature 'FixRobModel,fiUnOvShoot'
optIC(model, risk, sampleSize, upper = 1e4, lower = 1e-4,
                                          maxiter = 50, tol = .Machine$double.eps^0.4, 
                                          withMakeIC = FALSE, warn = TRUE,
                                          Algo = "A", cont = "left",
                                          verbose = NULL, modifyICwarn = NULL, ...)

Arguments

Details

In case of the finite-sample risk "fiUnOvShoot" one can choose between two algorithms for the computation of this risk where the least favorable contamination is assumed to be left or right of some bound. For more details we refer to Section 11.3 of Kohl (2005).

Value

Some optimally robust IC is computed.

Methods

model = "InfRobModel", risk = "asRisk"

computes optimally robust influence curve for robust models with infinitesimal neighborhoods and various asymptotic risks.

model = "InfRobModel", risk = "asUnOvShoot"

computes optimally robust influence curve for robust models with infinitesimal neighborhoods and asymptotic under-/overshoot risk.

model = "FixRobModel", risk = "fiUnOvShoot"

computes optimally robust influence curve for robust models with fixed neighborhoods and finite-sample under-/overshoot risk.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

Kohl, M. and Ruckdeschel, P. (2010): R package distrMod: Object-Oriented Implementation of Probability Models. J. Statist. Softw. 35(10), 1–27. doi:10.18637/jss.v035.i10.

Kohl, M. and Ruckdeschel, P., and Rieder, H. (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333–354. doi:10.1007/s10260-010-0133-0.

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer. doi:10.1007/978-1-4684-0624-5.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2008) The Costs of not Knowing the Radius. Statistical Methods and Applications 17(1) 13-40. doi:10.1007/s10260-007-0047-7.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2001) The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under doi:10.18452/3638.

See Also

InfluenceCurve-class, RiskType-class

Examples

B <- BinomFamily(size = 25, prob = 0.25) 

## classical optimal IC
IC0 <- optIC(model = B, risk = asCov())
plot(IC0) # plot IC
checkIC(IC0, B)

Generic function for the computation of the minimal risk

Description

Generic function for the computation of the optimal (i.e., minimal) risk for a probability model.

Usage

optRisk(model, risk, ...)

## S4 method for signature 'L2ParamFamily,asCov'
optRisk(model, risk)

## S4 method for signature 'InfRobModel,asRisk'
optRisk(model, risk, z.start = NULL,
                   A.start = NULL, upper = 1e4, maxiter = 50,
                   tol = .Machine$double.eps^0.4, warn = TRUE, noLow = FALSE)

## S4 method for signature 'FixRobModel,fiUnOvShoot'
optRisk(model, risk, sampleSize,
                   upper = 1e4, maxiter = 50, tol = .Machine$double.eps^0.4,
                   warn = TRUE, Algo = "A", cont = "left")

Arguments

Details

In case of the finite-sample risk "fiUnOvShoot" one can choose between two algorithms for the computation of this risk where the least favorable contamination is assumed to be left or right of some bound. For more details we refer to Section 11.3 of Kohl (2005).

Value

The minimal risk is computed.

Methods

model = "L2ParamFamily", risk = "asCov"

asymptotic covariance of L2 differentiable parameteric family.

model = "InfRobModel", risk = "asRisk"

asymptotic risk of a infinitesimal robust model.

model = "FixRobModel", risk = "fiUnOvShoot"

finite-sample under-/overshoot risk of a robust model with fixed neighborhood.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

RiskType-class

Examples

optRisk(model = NormLocationScaleFamily(), risk = asCov())

Methods for Function plot in Package ‘ROptEst’

Description

plot-methods

Details

S4-Method plot for for signature IC,missing has been enhanced compared to its original definition in RobAStBase so that if argument MBRB is NA, it is filled automatically by a call to optIC which computes the MBR-IC on the fly. To this end, there is an additional argument n.MBR defaulting to 10000 to determine the number of evaluation points. points.

Examples

N <- NormLocationScaleFamily(mean=0, sd=1)
IC <- optIC(model = N, risk = asCov())
## Don't run to reduce check time on CRAN

plot(IC, main = TRUE, panel.first= grid(),
     col = "blue", cex.main = 2, cex.inner = 0.6,
     withMBR=TRUE)

Generic function for the computation of the radius minimax IC

Description

Generic function for the computation of the radius minimax IC.

Usage

radiusMinimaxIC(L2Fam, neighbor, risk, ...)

## S4 method for signature 'L2ParamFamily,UncondNeighborhood,asGRisk'
radiusMinimaxIC(
        L2Fam, neighbor, risk, loRad = 0, upRad = Inf, z.start = NULL, A.start = NULL, 
        upper = NULL, lower = NULL, OptOrIter = "iterate",
        maxiter = 50, tol = .Machine$double.eps^0.4,
        warn = FALSE, verbose = NULL, loRad0 = 1e-3, ...,
        returnNAifProblem = FALSE, loRad.s = NULL, upRad.s = NULL,
        modifyICwarn = NULL)

Arguments

Details

In case the neighborhood radius is unknown, Rieder et al. (2001, 2008) and Kohl (2005) show that there is nevertheless a way to compute an optimally robust IC - the so-called radius-minimax IC - which is optimal for some radius interval.

Value

The radius minimax IC is computed.

Methods

L2Fam = "L2ParamFamily", neighbor = "UncondNeighborhood", risk = "asGRisk":

computation of the radius minimax IC for an L2 differentiable parametric family.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

H. Rieder, M. Kohl, and P. Ruckdeschel (2008). The Costs of not Knowing the Radius. Statistical Methods and Applications, 17(1) 13-40. doi:10.1007/s10260-007-0047-7.

H. Rieder, M. Kohl, and P. Ruckdeschel (2001). The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under doi:10.18452/3638.

P. Ruckdeschel (2005). Optimally One-Sided Bounded Influence Curves. Mathematical Methods of Statistics 14(1), 105-131.

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

See Also

radiusMinimaxIC

Examples

N <- NormLocationFamily(mean=0, sd=1) 
radIC <- radiusMinimaxIC(L2Fam=N, neighbor=ContNeighborhood(), 
                         risk=asMSE(), loRad=0.1, upRad=0.5)
checkIC(radIC)

Optimally robust estimation

Description

Function to compute optimally robust estimates for L2-differentiable parametric families via k-step construction.

Usage

robest(x, L2Fam,  fsCor = 1, risk = asMSE(), steps = 1L,
        verbose = NULL, OptOrIter = "iterate", nbCtrl = gennbCtrl(),
        startCtrl = genstartCtrl(), startICCtrl = genstartICCtrl(),
        kStepCtrl = genkStepCtrl(), na.rm = TRUE, ..., debug = FALSE,
        withTimings = FALSE, diagnostic = FALSE)

Arguments

Details

A new, more structured interface to the former function roptest. For details, see this function.

In some respects this functions allows for more granular arguments, in the sense that the different steps (a) computation of the inital estimator, resp. (a') in case initial.est is missing computation of the initial MDE, (b) computation of the optimal IC and (c) computation of the k-step estimator each can have individial arguments E.arglist to be passed on to calls to expectation operator E within each step.

These different arguments are passed through the input generating functions genstartCtrl, genstartICCtrl, and kStepCtrl

Diagnostics on the involved integrations are available if argument diagnostic is TRUE. Then there are attributes diagnostic and kStepDiagnostic attached to the return value, which may be inspected and assessed through showDiagnostic and getDiagnostic.

Value

Object of class "kStepEstimate". In addition, it has an attribute "timings" where computation time is stored.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

Kohl, M. and Ruckdeschel, P. (2010): R package distrMod: Object-Oriented Implementation of Probability Models. J. Statist. Softw. 35(10), 1–27. doi:10.18637/jss.v035.i10.

Kohl, M. and Ruckdeschel, P., and Rieder, H. (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333–354. doi:10.1007/s10260-010-0133-0.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer. doi:10.1007/978-1-4684-0624-5.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2008) The Costs of not Knowing the Radius. Statistical Methods and Applications 17(1) 13-40. doi:10.1007/s10260-007-0047-7.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2001) The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under doi:10.18452/3638

See Also

roblox, L2ParamFamily-class UncondNeighborhood-class, RiskType-class

Examples

## Don't test to reduce check time on CRAN

#############################
## 1. Binomial data
#############################
## generate a sample of contaminated data
set.seed(123)
ind <- rbinom(100, size=1, prob=0.05)
x <- rbinom(100, size=25, prob=(1-ind)*0.25 + ind*0.9)

## Family
BF <- BinomFamily(size = 25)
## ML-estimate
MLest <- MLEstimator(x, BF)
estimate(MLest)
confint(MLest)

## compute optimally robust estimator (known contamination)
nb <- gennbCtrl(eps=0.05)
robest1 <- robest(x, BF, nbCtrl = nb, steps = 3)
estimate(robest1)

confint(robest1, method = symmetricBias())
## neglecting bias
confint(robest1)
plot(pIC(robest1))
tmp <- qqplot(x, robest1, cex.pch=1.5, exp.cex2.pch = -.25,
              exp.fadcol.pch = .55, jit.fac=.9)

## compute optimally robust estimator (unknown contamination)
nb2 <- gennbCtrl(eps.lower = 0, eps.upper = 0.2)
robest2 <- robest(x, BF, nbCtrl = nb2, steps = 3)
estimate(robest2)
confint(robest2, method = symmetricBias())
plot(pIC(robest2))

## total variation neighborhoods (known deviation)
nb3 <- gennbCtrl(eps = 0.025, neighbor = TotalVarNeighborhood())
robest3 <- robest(x, BF, nbCtrl = nb3, steps = 3)
estimate(robest3)
confint(robest3, method = symmetricBias())
plot(pIC(robest3))

## total variation neighborhoods (unknown deviation)
nb4 <- gennbCtrl(eps.lower = 0, eps.upper = 0.1,
                 neighbor = TotalVarNeighborhood())
robest3 <- robest(x, BF, nbCtrl = nb4, steps = 3)
robest4 <- robest(x, BinomFamily(size = 25), nbCtrl = nb4, steps = 3)
estimate(robest4)
confint(robest4, method = symmetricBias())
plot(pIC(robest4))


#############################
## 2. Poisson data
#############################
## Example: Rutherford-Geiger (1910); cf. Feller~(1968), Section VI.7 (a)
x <- c(rep(0, 57), rep(1, 203), rep(2, 383), rep(3, 525), rep(4, 532), 
       rep(5, 408), rep(6, 273), rep(7, 139), rep(8, 45), rep(9, 27), 
       rep(10, 10), rep(11, 4), rep(12, 0), rep(13, 1), rep(14, 1))

## Family
PF <- PoisFamily()

## ML-estimate
MLest <- MLEstimator(x, PF)
estimate(MLest)
confint(MLest)

## compute optimally robust estimator (unknown contamination)
nb1 <- gennbCtrl(eps.upper = 0.1)
robest <- robest(x, PF, nbCtrl = nb1, steps = 3)
estimate(robest)

confint(robest, symmetricBias())
plot(pIC(robest))
tmp <- qqplot(x, robest, cex.pch=1.5, exp.cex2.pch = -.25,
              exp.fadcol.pch = .55, jit.fac=.9)
 
## total variation neighborhoods (unknown deviation)
nb2 <- gennbCtrl(eps.upper = 0.05, neighbor = TotalVarNeighborhood())
robest1 <- robest(x, PF, nbCtrl = nb2, steps = 3)
estimate(robest1)
confint(robest1, symmetricBias())
plot(pIC(robest1))


#############################
## 3. Normal (Gaussian) location and scale
#############################

## this example of a two dimensional parameter
## to be estimated will need more time than 
## 5 seconds to run 
## you can find it in 
## system.file("scripts", "examples_taking_longer.R", 
##              package="ROptEst")

Optimally robust estimation

Description

Function to compute optimally robust estimates for L2-differentiable parametric families via k-step construction.

Usage

roptest(x, L2Fam, eps, eps.lower, eps.upper, fsCor = 1, initial.est, 
        neighbor = ContNeighborhood(), risk = asMSE(), steps = 1L, 
        distance = CvMDist, startPar = NULL, verbose = NULL,
        OptOrIter = "iterate",
        useLast = getRobAStBaseOption("kStepUseLast"),
        withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
        IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
        withICList = getRobAStBaseOption("withICList"),
        withPICList = getRobAStBaseOption("withPICList"),
        na.rm = TRUE, initial.est.ArgList, ...,
        withLogScale = TRUE, ..withCheck = FALSE, withTimings = FALSE,
        withMDE = NULL, withEvalAsVar = NULL, withMakeIC = FALSE,
        modifyICwarn = NULL, E.argList = NULL, diagnostic = FALSE)
roptest.old(x, L2Fam, eps, eps.lower, eps.upper, fsCor = 1, initial.est,
        neighbor = ContNeighborhood(), risk = asMSE(), steps = 1L,
        distance = CvMDist, startPar = NULL, verbose = NULL,
        OptOrIter = "iterate",
        useLast = getRobAStBaseOption("kStepUseLast"),
        withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
        IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
        withICList = getRobAStBaseOption("withICList"),
        withPICList = getRobAStBaseOption("withPICList"),
        na.rm = TRUE, initial.est.ArgList, ...,
        withLogScale = TRUE)

Arguments

Details

Computes the optimally robust estimator for a given L2 differentiable parametric family. The computation uses a k-step construction with an appropriate initial estimate; cf. also kStepEstimator. Valid candidates are e.g. Kolmogorov(-Smirnov) or von Mises minimum distance estimators (default); cf. Rieder (1994) and Kohl (2005).

Before package version 0.9, this computation was done with the code of function roptest.old (with the same formals). From package version 0.9 on, this function uses the modularized function robest internally.

If the amount of gross errors (contamination) is known, it can be specified by eps. The radius of the corresponding infinitesimal contamination neighborhood is obtained by multiplying eps by the square root of the sample size.

If the amount of gross errors (contamination) is unknown, try to find a rough estimate for the amount of gross errors, such that it lies between eps.lower and eps.upper.

In case eps.lower is specified and eps.upper is missing, eps.upper is set to 0.5. In case eps.upper is specified and eps.lower is missing, eps.lower is set to 0.

If neither eps nor eps.lower and/or eps.upper is specified, eps.lower and eps.upper are set to 0 and 0.5, respectively.

If eps is missing, the radius-minimax estimator in sense of Rieder et al. (2001, 2008), respectively Section 2.2 of Kohl (2005) is returned.

Finite-sample and higher order results suggest that the asymptotically optimal procedure is to liberal. Using fsCor the radius can be modified - as a rule enlarged - to obtain a more conservative estimate. In case of normal location and scale there is function finiteSampleCorrection which returns a finite-sample corrected (enlarged) radius based on the results of large Monte-Carlo studies.

The logic in argument initial.est is as follows: It can be a numeric vector of the length of the unknow parameter or a function or it can be missing. If it is missing, one consults argument startPar for a search interval (if a one dimensional unknown parameter) or a starting value for the search (if the dimension of the unknown parameter is larger than one). If startPar is missing, too, it takes the value from the corresponding slot of argument L2Fam. Then, if argument withMDE is TRUE a Minimum-Distance estimator is computed as initial value initial.est with distance as specified in argument distance and possibly further arguments as passed through ....

In the next step, the value of initial.est (either if not missing from beginning or as computed through the MDE) is then passed on to kStepEstimator.start which then takes out the essential information for the sequel, i.e., a numeric vector of the estimate.

At this initial value the optimal influence curve is computed through interface getStartIC, which in turn, depending on the risk calls optIC, radiusMinimaxIC, or computes the IC from precomputed grid values in case of risk being of class interpolRisk. With the obtained optimal IC, kStepEstimator is called.

The default value of argument useLast is set by the global option kStepUseLast which by default is set to FALSE. In case of general models useLast remains unchanged during the computations. However, if slot CallL2Fam of IC generates an object of class "L2GroupParamFamily" the value of useLast is changed to TRUE. Explicitly setting useLast to TRUE should be done with care as in this situation the influence curve is re-computed using the value of the one-step estimate which may take quite a long time depending on the model.

If useLast is set to TRUE the computation of asvar, asbias and IC is based on the k-step estimate.

Timings for the steps run through in roptest are available in attributes timings, and for the step of the kStepEstimator in kStepTimings.

One may also use the arguments startCtrl, startICCtrl, and kStepCtrl of function robest. This allows for individual settings of E.argList, withEvalAsVar, and withMakeIC for the different steps. If any of the three arguments startCtrl, startICCtrl, and kStepCtrl is used, the respective attributes set in the correspondig argument are used and, if colliding with arguments directly passed to roptest, the directly passed ones are ignored.

Diagnostics on the involved integrations are available if argument diagnostic is TRUE. Then there are attributes diagnostic and kStepDiagnostic attached to the return value, which may be inspected and assessed through showDiagnostic and getDiagnostic.

Value

Object of class "kStepEstimate". In addition, it has an attribute "timings" where computation time is stored.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

Kohl, M. and Ruckdeschel, P. (2010): R package distrMod: Object-Oriented Implementation of Probability Models. J. Statist. Softw. 35(10), 1–27. doi:10.18637/jss.v035.i10.

Kohl, M. and Ruckdeschel, P., and Rieder, H. (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333–354. doi:10.1007/s10260-010-0133-0.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer. doi:10.1007/978-1-4684-0624-5.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2008) The Costs of not Knowing the Radius. Statistical Methods and Applications 17(1) 13-40. doi:10.1007/s10260-007-0047-7.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2001) The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under doi:10.18452/3638

See Also

roblox, L2ParamFamily-class UncondNeighborhood-class, RiskType-class

Examples

## Don't run to reduce check time on CRAN
## Not run: 
#############################
## 1. Binomial data
#############################
## generate a sample of contaminated data
set.seed(123)
ind <- rbinom(100, size=1, prob=0.05)
x <- rbinom(100, size=25, prob=(1-ind)*0.25 + ind*0.9)

## ML-estimate
MLest <- MLEstimator(x, BinomFamily(size = 25))
estimate(MLest)
confint(MLest)

## compute optimally robust estimator (known contamination)
robest1 <- roptest(x, BinomFamily(size = 25), eps = 0.05, steps = 3)
robest1.0 <- roptest.old(x, BinomFamily(size = 25), eps = 0.05, steps = 3)
identical(robest1,robest1.0)
estimate(robest1)
confint(robest1, method = symmetricBias())
## neglecting bias
confint(robest1)
plot(pIC(robest1))
tmp <- qqplot(x, robest1, cex.pch=1.5, exp.cex2.pch = -.25,
              exp.fadcol.pch = .55, jit.fac=.9)

## compute optimally robust estimator (unknown contamination)
robest2 <- roptest(x, BinomFamily(size = 25), eps.lower = 0, eps.upper = 0.2, steps = 3)
estimate(robest2)
confint(robest2, method = symmetricBias())
plot(pIC(robest2))

## total variation neighborhoods (known deviation)
robest3 <- roptest(x, BinomFamily(size = 25), eps = 0.025, 
                   neighbor = TotalVarNeighborhood(), steps = 3)
estimate(robest3)
confint(robest3, method = symmetricBias())
plot(pIC(robest3))

## total variation neighborhoods (unknown deviation)
robest4 <- roptest(x, BinomFamily(size = 25), eps.lower = 0, eps.upper = 0.1, 
                   neighbor = TotalVarNeighborhood(), steps = 3)
estimate(robest4)
confint(robest4, method = symmetricBias())
plot(pIC(robest4))

#############################
## 2. Poisson data
#############################
## Example: Rutherford-Geiger (1910); cf. Feller~(1968), Section VI.7 (a)
x <- c(rep(0, 57), rep(1, 203), rep(2, 383), rep(3, 525), rep(4, 532), 
       rep(5, 408), rep(6, 273), rep(7, 139), rep(8, 45), rep(9, 27), 
       rep(10, 10), rep(11, 4), rep(12, 0), rep(13, 1), rep(14, 1))

## ML-estimate
MLest <- MLEstimator(x, PoisFamily())
estimate(MLest)
confint(MLest)

## compute optimally robust estimator (unknown contamination)
robest <- roptest(x, PoisFamily(), eps.upper = 0.1, steps = 3)
estimate(robest)
confint(robest, symmetricBias())

plot(pIC(robest))
tmp <- qqplot(x, robest, cex.pch=1.5, exp.cex2.pch = -.25,
              exp.fadcol.pch = .55, jit.fac=.9)
 
## total variation neighborhoods (unknown deviation)
robest1 <- roptest(x, PoisFamily(), eps.upper = 0.05, 
                  neighbor = TotalVarNeighborhood(), steps = 3)
estimate(robest1)
confint(robest1, symmetricBias())
plot(pIC(robest1))

## End(Not run)

#############################
## 3. Normal (Gaussian) location and scale
#############################

## this example of a two dimensional parameter
## to be estimated will need more time than 
## 5 seconds to run 
## you can find it in 
## system.file("scripts", "examples_taking_longer.R", 
##              package="ROptEst")

Methods for Function updateNorm in Package ‘ROptEst’

Description

updateNorm-methods to update norm in IC-Algo

Usage

updateNorm(normtype, ...)
## S4 method for signature 'SelfNorm'
updateNorm(normtype, L2, neighbor, biastype, Distr, V.comp, 
                                cent, stand,  w)     

Arguments

Details

updateNorm is used internally in the opt-IC-algorithm to be able to work with a norm that depends on the current covariance (SelfNorm)

Value

Methods

updateNorm

signature(normtype = "SelfNorm"): udates the norm in the self-standardized case; just used internally in the opt-IC-Algorithm.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

See Also

NormType-class