| Type: | Package |
| Title: | Multiple Testing of Local Extrema for Detection of Change Points |
| Version: | 1.0-1 |
| Date: | 2019-09-1 |
| Author: | Zhibing He and Dan Cheng |
| Maintainer: | Zhibing He <zhibingh@asu.edu> |
| Description: | A new approach to detect change points based on smoothing and multiple testing, which is for long data sequence modeled as piecewise constant functions plus stationary Gaussian noise, see Dan Cheng and Armin Schwartzman (2015) <doi:10.48550/arXiv.1504.06384>. |
| Depends: | R (≥ 3.1.0) |
| Imports: | parallel, foreach, doParallel, latex2exp |
| URL: | https://arxiv.org/abs/1504.06384 |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 6.1.1 |
| NeedsCompilation: | no |
| Packaged: | 2019-09-26 19:40:58 UTC; hzb |
| Repository: | CRAN |
| Date/Publication: | 2019-10-02 10:00:05 UTC |
Evaluate performance of estimated change points
Description
Evaluate performance of estimated change points
Usage
Fdr(uh, b, th)
Arguments
uh |
a vector of estimated change points locations |
b |
a scalar of location tolerance, specified by user |
th |
a vector of true change points locations |
Value
a list of vector of FDR and Power
FDR |
a scalar of fdr (false discovery rate) |
Power |
a scalar of power (true positive rate) |
See Also
Examples
Fdr(uh=c(7,15,32,47),b=4,th=c(10,20,30,40,50))
Generate first-order differential of a smoothed sequence Y
Description
Generate first-order differential of a smoothed sequence Y
Usage
GenDY(mu, z, gamma)
Arguments
mu |
a vector of piecewise constant |
z |
a vector of stationary Gaussian random error |
gamma |
bandwidth of nonparameter smoothing |
Value
a vector of the differential of Y
See Also
Examples
mu = GenMu(x=1:10,pos=seq(10,100,10),size=150)
z = GenZ(nu=2,size=150)
GenDY(mu=mu,z=z,gamma=4)
Generate a piecewise constant sequence starting from 0
Description
Generate a piecewise constant sequence starting from 0
Usage
GenMu(x, pos, size)
Arguments
x |
a vector containing all values of change points |
pos |
positions of change points, corresponding to |
size |
sample size |
Value
a piecewise constant sequence
See Also
Examples
GenMu(x=1:10,pos=seq(10,100,10),size=150)
Generate Gaussian autocorrelated random error sequence based on White-noise and Gaussian kernal
Description
Generate Gaussian autocorrelated random error sequence based on White-noise and Gaussian kernal
Usage
GenZ(nu, size)
Arguments
nu |
bandwidth of Gaussian kernal applied to White-noise, Whitenoise error if |
size |
sample size |
Value
a vector of random error
See Also
Examples
GenZ(nu=2,size=1000)
Estimate s2,lambda2,lambda4,Delta
Description
Estimate s2,lambda2,lambda4,Delta
Usage
ch.est(nu, gamma, size, B = 100)
Arguments
nu |
bandwidth of Gaussian kernal applied to White-noise, Whitenoise error if |
gamma |
bandwidth of nonparameter smoothing |
size |
sample size |
B |
Montelarlo iteration times |
Value
a list of s2,lambda2,lambda4,Delta
References
Multiple Testing of Local Extrema for Detection of Change Points https://arxiv.org/abs/1504.06384
See Also
Examples
ch.est(nu=2,gamma=4,size=1000,B=100)
Compute convolution function using FFT, similar to the function 'conv' in matlab
Description
Compute convolution function using FFT, similar to the function 'conv' in matlab
Usage
conv(u, v, shape = c("same", "full"))
Arguments
u |
vector |
v |
vector |
shape |
if 'same', return central part of the convolution,the same size as u; ortherwise return the whole sequence with size lenth(u)+length(v)-1 |
Value
a vector of convolution, as specified by shape.
References
Matlab document on 'conv' https://www.mathworks.com/help/matlab/ref/conv.html
Examples
u = c(-1,2,3,-2,0,1,2)
v = c(2,4,-1,1)
w = conv(u,v,'same')
Parallel computing fdr and power of change points estimation for different gamma and nu
Description
Parallel computing fdr and power of change points estimation for different gamma and nu
Usage
fdr.gam(c, mu, Gamma, Nu, b, th, B = 100, level = 0.1, iter = 100)
Arguments
c |
number of cpu cores used for parallel computing |
mu |
a vector of piecewise constant |
Gamma |
a vector of different |
Nu |
a vector of different |
b |
a scalar of location tolerance, specified by user |
th |
a vector of true change points locations |
B |
Montelarlo iteration times |
level |
FDR control level |
iter |
iteration times for each combination of |
Value
a list of matrix with the same length as Nu, FDR and Power for different Gamma are displayed within each matrix
Examples
size=12000
a = 1
A = a*(1:119)
H = seq(100,11900,100)
mu = GenMu(A,H,size=size)
z = GenZ(nu=2,size=size)
Gamma = seq(1,5,1)
Nu = seq(0,2,0.5)
model = fdr.gam(2,mu,Gamma,Nu,8,H,iter=100)
FDR threshold based on the Benjamini-Hochberg algorithm
Description
FDR threshold based on the Benjamini-Hochberg algorithm
Usage
fdrBH(p, q)
Arguments
p |
a vector of p-values |
q |
False Discovery Rate level |
Value
p-value threshold based on independence or positive dependence
See Also
Examples
fdrBH(seq(0.01,0.1,0.01),q=0.1)
Illustration plot of the procedure t0 detect change points
Description
Illustration plot of the procedure t0 detect change points
Usage
illu.plot(mu, z, gamma, whichcp, b, Tmax, Tmin)
Arguments
mu |
a vector of piecewise constant |
z |
a vector of stationary Gaussian random error |
gamma |
bandwidth of nonparameter smoothing |
whichcp |
output of the function |
b |
a scalar of location tolerance, specified by user |
Tmax |
a vector of true peak locations |
Tmin |
a vector true valley locations |
Value
a figure plot showing detection of change points
Examples
set.seed(2019)
L = 1200
A = c(2.8,0,-2.4,0,-3,0.5,3,5,2,0)/1.5
Tmax = c(150,410,680,770,980)
Tmin = c(250,320,550,1000,1100)
H = c(150,250,320,410,550,680,770,980,1000,1100)
mu = GenMu(A,H,L); z = GenZ(nu=2,L)
y1 = GenDY(mu=mu,z=z,gamma=6)
chest = ch.est(nu=2,gamma=6,size=L,B=100)
chp= which.cp(y1,chest,level=0.1)
illu.plot(mu,z,gamma=6,chp,b=5,Tmax,Tmin)
Find locations of change points
Description
Find locations of change points
Usage
which.cp(y1, chest, level = 0.1)
Arguments
y1 |
a vector of the differential of sequence Y |
chest |
output of function |
level |
FDR control level |
Value
a list of components
peak |
a vector of peaks location |
vall |
a vector of valleys location |
pval |
a scalar of adjusted p-value based on FDR control |
thresh |
a scalar of threshold for |
See Also
Examples
mu = GenMu(x=1:10,pos=seq(10,100,10),size=150)
z = GenZ(nu=2,size=150)
y1 = GenDY(mu,z,gamma=4)
chest = ch.est(nu=2,gamma=8,size=150,B=100)
which.cp(y1,chest,level=0.1)
Find local maxima and minima in a sequence
Description
Find local maxima and minima in a sequence
Usage
which.peaks(x, partial = FALSE, decreasing = FALSE)
Arguments
x |
a vector with maxima or minima |
partial |
endpoints will be considered if 'true' |
decreasing |
find local minima if 'true', ortherwise local maxima |
Value
a vector of positions of local maxima or minima
Examples
a = 100:1
which.peaks(a*sin(a/3))