Title: Smooth-Rough Partitioning of the Regression Coefficients
Version: 1.2.0
Description: Performs the change-point detection in regression coefficients of linear model by partitioning the regression coefficients into two classes of smoothness. The change-point and the regression coefficients are jointly estimated.
Depends: R (≥ 3.4.0)
License: GPL-2 | GPL-3 [expanded from: GPL]
LazyData: true
Imports: fda, mgcv
Encoding: UTF-8
NeedsCompilation: no
RoxygenNote: 6.1.0
Packaged: 2019-04-18 16:10:47 UTC; maengh
Author: Hyeyoung Maeng [aut, cre], Piotr Fryzlewicz [aut]
Maintainer: Hyeyoung Maeng <h.maeng@lse.ac.uk>
Repository: CRAN
Date/Publication: 2019-04-24 08:40:03 UTC

srp: Detecting the change-point of smoothness in linear regression coefficients

Description

The srp package performs the change-point detection in regression coefficients of a linear model by partitioning the regression coefficients into two classes of smoothness. To start with, see the function srp.c.

Author(s)

Hyeyoung Maeng, h.maeng@lse.ac.uk

References

"Regularised forecasting via smooth-rough partitioning of the regression coefficients", H. Maeng and P. Fryzlewicz (2018), preprint.

See Also

srp.c

The natural cubic spline interpolation

Description

This function performs the natural cubic spline interpolation of a design matrix.

Usage

ncs(x)

Arguments

x

The design matrix.

Details

Usually only called by srp.c and srp.l.

Value

cf0

The coefficient matrix for B-splines obtained by natural cubic spline interpolation of x.

Author(s)

Hyeyoung Maeng, h.maeng@lse.ac.uk

See Also

srp.c, srp.l

Examples

x <- matrix(rnorm(100), ncol=10)
ncs(x)$cf0

The Smooth-Rough Partition model prediction

Description

This function performs the predictions from the results of Smooth-Rough Partition fitting.

Usage

## S3 method for class 'srp.c'
predict(object, x, ...)

Arguments

object

An object of class either 'srp.c', returned by srp.c.

x

A new matrix you wish to fit Smooth-Rough Partition model. The dimension of row is the number of covariates.

...

Further parameters that can be passed to predict.srp.c.

Details

The Smooth-Rough Partition model is described in "Regularised forecasting via smooth-rough partitioning of the regression coefficients", H. Maeng and P. Fryzlewicz (2018), preprint.

Value

yhat

The vector of predicted values.

Author(s)

Hyeyoung Maeng, h.maeng@lse.ac.uk

See Also

sic.c, srp.c

The Smooth-Rough Partition model prediction

Description

This function performs the predictions from the results of Smooth-Rough Partition fitting.

Usage

## S3 method for class 'srp.l'
predict(object, x, ...)

Arguments

object

An object of class 'srp.l', returned by srp.l.

x

A new matrix you wish to fit Smooth-Rough Partition model. The dimension of row is the number of covariates.

...

Further parameters that can be passed to predict.srp.l.

Details

The Smooth-Rough Partition model is described in "Regularised forecasting via smooth-rough partitioning of the regression coefficients", H. Maeng and P. Fryzlewicz (2018), preprint.

Value

yhat

The vector of predicted values.

Author(s)

Hyeyoung Maeng, h.maeng@lse.ac.uk

See Also

sic.l, srp.l

Optimisation of the Smooth-Rough Partition model

Description

This function performs the optimisation of the number of unconstrained regression parameters in Smooth-Rough Partition model by minimising SIC criterion and gives the change-point of smoothness in regression parameters.

Usage

sic.c(x.basis = x.basis, B.basis = B.basis, x = x, y = y,
  cf0 = cf0, maxq = maxq, fixedq = F, L = L, inisp = inisp)

Arguments

x.basis

The b-spline basis defined for interpolated x in srp.c

B.basis

The b-spline basis defined for constrained regression coefficient.

x

The design matrix used in srp.c.

y

The response variable used in srp.c.

cf0

The coefficient matrix obtained by natural cubic spline interpolation of x in ncs.

maxq

The maximum number of unconstrained parameters if fixedq is FALSE. Otherwise, it is considered as a unique number of unconstrained parameters.

fixedq

If TRUE, maxq is considered as a fixed number of unconstrained parameters and if FALSE, maxq is a maximum and a sequence of possible values are investigated to select the optimal.

L

The dimension of b-spline expansion for constrained parameters used in srp.c.

inisp

The initial value for the optimisation of tuning parameters in srp.c.

Details

Usually only called by srp.c.

Value

The following components are obtained only when fixedq is FALSE:

qhat

The optimal number of unconstrained parameters.

sicq

The vector of Schwarz criterion with length maxq which is computed for the different number of unconstrained parameters.

The following components are obtained only when fixedq is TRUE:

muhat

The estimator of constant parameter.

bhat

The vector of evaluated constrained functional regression coefficient.

ahat

The vector of unconstrained regression coefficient estimators.

etahat

The vector containing both bhat and ahat with unevaluated form.

yhat

The vector of estimated response variable.

sp

The vector of two tuning parameters estimated by minimising generalised cross validation (GCV).

L

The number of b-spline bases used for constrained regression parameters.

Author(s)

Hyeyoung Maeng, h.maeng@lse.ac.uk

See Also

sic.l, predict.srp.c, srp.c

Examples

library(fda)
x <- matrix(rnorm(10000), ncol=100)
y <- matrix(rnorm(100), ncol=1)
p <- dim(x)[1] + 1
t <- seq(0, 1, length.out=dim(x)[1])*(dim(x)[1])
x.basis <- as.fd(splinefun(t, x[, 1], method="natural"))$basis
B.basis <- create.bspline.basis(rangeval=c(0, dim(x)[1]), norder=4, nbasis=35)
result <- sic.c(x.basis=x.basis, B.basis=B.basis, x=x, y=y, cf0=ncs(x)$cf0, maxq=10, L=35, inisp=1)
plot(result$sicq, type="b")

Optimisation of the (simpler) Smooth-Rough Partition model

Description

This function performs the optimisation of the number of unconstrained regression parameters in (simpler) Smooth-Rough Partition model by minimising SIC criterion and gives the change-point in regression parameters.

Usage

sic.l(x.basis = x.basis, M.basis = M.basis, x = x, y = y,
  cf0 = cf0, maxq = maxq, fixedq = F)

Arguments

x.basis

The b-spline basis defined for interpolated x in srp.l.

M.basis

The monomial basis defined for constrained regression coefficient.

x

The design matrix used in srp.l.

y

The response variable used in srp.l.

cf0

The coefficient matrix obtained by natural cubic spline interpolation of x in ncs.

maxq

The maximum number of unconstrained parameters if fixedq is FALSE. Otherwise, it is considered as a unique number of unconstrained parameters.

fixedq

If TRUE, maxq is considered as a fixed number of unconstrained parameters and if FALSE, maxq is a maximum and a sequence of possible values are investigated to select the optimal.

Details

Usually only called by srp.l.

Value

The following components are obtained only when fixedq is FALSE:

qhat

The optimal number of unconstrained parameters.

sicq

The vector of Schwarz criterion with length maxq which is computed for the different number of unconstrained parameters.

The following components are obtained only when fixedq is TRUE:

muhat

The estimator of constant parameter.

bhat

The vector of evaluated constrained functional regression coefficient.

ahat

The vector of unconstrained regression coefficient estimators.

etahat

The vector containing both bhat and ahat with unevaluated form.

yhat

The vector of estimated response variable.

Author(s)

Hyeyoung Maeng, h.maeng@lse.ac.uk

See Also

sic.c, srp.l

Examples

library(fda)
x <- matrix(rnorm(10000), ncol=100)
y <- matrix(rnorm(100), ncol=1)
p <- dim(x)[1] + 1
t <- seq(0, 1, length.out=dim(x)[1])*(dim(x)[1])
x.basis <- as.fd(splinefun(t, x[, 1], method="natural"))$basis
M.basis <- create.monomial.basis(rangeval=c(0, dim(x)[1]), nbasis=2)
result <- sic.l(x.basis=x.basis, M.basis=M.basis, x=x, y=y, cf0=ncs(x)$cf0, maxq=10)
plot(result$sicq, type="b")

The Smooth-Rough Partition model fitting

Description

This function performs the Smooth-Rough Partition linear regression with the input matrix.

Usage

srp.c(x, y, maxq = max(30, ceiling(0.1 * dim(x)[1])), L = 35,
  norder = 4, inisp = 1, plot = T)

Arguments

x

A matrix you wish to fit Smooth-Rough Partition model. The dimension of row is the number of variables which are pre-ordered in terms of their importance in prediction.

y

A vector you wish to use as a response variable in case of regressing y on x. If y is missing, the response variable is obtained from the last row of x.

maxq

An integer specifying the maximum number of unconstrained parameters which the model can have. The default is max(30, ceiling(0.1*dim(x)[1])).

L

An integer specifying the dimension of b-spline expansion for the constrained (smoothed) parameters. The default is 35.

norder

An integer specifying the order of b-splines. The default of 4 performs cubic splines.

inisp

An initial value for optimising the tuning parameters and the default is 1.

plot

If true, it gives the plot of estimated regression coefficients.

Details

The estimation procedure of Smooth-Rough Partition model is described in "Regularised forecasting via smooth-rough partitioning of the regression coefficients", H. Maeng and P. Fryzlewicz (2018), preprint.

Value

muhat

The estimator of constant parameter.

bhat

The vector of evaluated constrained functional regression coefficient.

ahat

The vector of unconstrained regression coefficient estimators.

etahat

The vector containing both bhat and ahat with unevaluated form.

yhat

The vector of estimated response variable.

SIC

The vector of Schwarz criterion with length maxq which is computed for the different number of unconstrained parameters.

qhat

The optimal number of unconstrained parameters selected in the model.

sp

The vector of two tuning parameters estimated by minimising generalised cross validation (GCV).

L

The number of bases used for constrained regression parameters.

norder

The order of b-splines specified.

Author(s)

Hyeyoung Maeng, h.maeng@lse.ac.uk

See Also

sic.c, predict.srp.c, srp.l

Examples

x <- matrix(rnorm(10000), ncol=100)
srp.c(x)

The (simpler) Smooth-Rough Partition linear regression model fitting

Description

This function performs same as srp.c except that constrained functional coefficient is estimated as a linear function.

Usage

srp.l(x, y, maxq = max(30, ceiling(0.1 * dim(x)[1])), plot = T)

Arguments

x

A matrix you wish to fit Smooth-Rough Partition model. The dimension of row is the number of variables which are pre-ordered in terms of their importance in prediction.

y

A vector you wish to use as a response variable in case of regressing y on x. If y is missing, the response variable is obtained from the last row of x.

maxq

An integer specifying the maximum number of unconstrained parameters which the model can have. The default is max(30, ceiling(0.1*dim(x)[1])).

plot

If true, it gives the plot of estimated regression coefficients.

Details

The estimation procedure of Smooth-Rough Partition model is described in "Regularised forecasting via smooth-rough partitioning of the regression coefficients", H. Maeng and P. Fryzlewicz (2018), preprint.

Value

muhat

The estimator of constant parameter.

bhat

The vector of evaluated constrained (linear) functional regression coefficient.

ahat

The vector of unconstrained regression coefficient estimators.

etahat

The vector containing both bhat and ahat with unevaluated form.

yhat

The vector of estimated response variable.

SIC

The vector of Schwarz criterion with length maxq which is computed for the different number of unconstrained parameters.

qhat

The optimal number of unconstrained parameters selected in the model.

Author(s)

Hyeyoung Maeng, h.maeng@lse.ac.uk

See Also

srp.c, predict.srp.l, sic.l

Examples

x <- matrix(rnorm(10000), ncol=100)
srp.l(x)

A dataset containing true regression coefficients for simulation

Description

True regression coefficients used for simulations in "Regularised forecasting via smooth-rough partitioning of the regression coefficients", H. Maeng and P. Fryzlewicz (2018), preprint.

Usage

data(truebeta)

Format

A matrix with 356 rows and 4 variables:

Case 1

true regression coefficients for case 1

Case 2

true regression coefficients for case 2

Case 3

true regression coefficients for case 3

Case 4

true regression coefficients for case 4