kerseg1 {kerSeg}

Kernel-based change-point detection for single change-point alternatives

Description

This function finds a break point in the sequence where the underlying distribution changes.

Usage

kerseg1(n, K, r1=1.2, r2=0.8, n0=0.05*n, n1=0.95*n,
   pval.appr=TRUE, skew.corr=TRUE, pval.perm=FALSE, B=100)

Arguments

n

The number of observations in the sequence.

K

The kernel matrix of observations in the sequence.

r1

The constant in the test statistics \textrm{Z}_{W,r1}(t).

r2

The constant in the test statistics \textrm{Z}_{W,r2}(t).

n0

The starting index to be considered as a candidate for the change-point.

n1

The ending index to be considered as a candidate for the change-point.

pval.appr

If it is TRUE, the function outputs the p-value approximation based on asymptotic properties.

skew.corr

This argument is useful only when pval.appr=TRUE. If skew.corr is TRUE, the p-value approximation would incorporate skewness correction.

pval.perm

If it is TRUE, the function outputs the p-value from doing B permutations, where B is another argument that you can specify. Doing permutation could be time consuming, so use this argument with caution as it may take a long time to finish the permutation.

B

This argument is useful only when pval.perm=TRUE. The default value for B is 100.

Value

Returns a list stat containing the each scan statistic, tauhat containing the estimated location of change-point, appr containing the approximated p-values of the fast tests when argument ‘pval.appr’ is TRUE, and perm containing the permutation p-values of the fast tests and GKCP when argument ‘pval.perm’ is TRUE. See below for more details.

seq

A vector of each scan statistic (standardized counts).

Zmax

The test statistics (maximum of the scan statistics).

tauhat

An estimate of the location of the change-point.

fGKCP1_bon

The p-value of \textrm{fGKCP}_{1} obtained by the Bonferroni procedure.

fGKCP1_sim

The p-value of \textrm{fGKCP}_{1} obtained by the Simes procedure.

fGKCP2_bon

The p-value of \textrm{fGKCP}_{2} obtained by the Bonferroni procedure.

fGKCP2_sim

The p-value of \textrm{fGKCP}_{2} obtained by the Simes procedure.

GKCP

The p-value of GKCP obtained by the random permutation.

See Also

kerSeg-package, kerseg1, gaussiankernel, kerseg2

Examples

## Sequence 1: change in the mean in the middle of the sequence.
d = 50
mu = 2
tau = 25
n = 50
set.seed(1)
y = rbind(matrix(rnorm(d*tau),tau), matrix(rnorm(d*(n-tau),mu/sqrt(d)), n-tau))
K = gaussiankernel(y) # Gaussian kernel matrix
a = kerseg1(n, K, pval.perm=TRUE, B=1000)
# output results based on the permutation and the asymptotic results.
# the scan statistics can be found in a$scanZ.
# the approximated p-values can be found in a$appr.
# the permutation p-values can be found in a$perm.

## Sequence 2: change in both the mean and variance away from the middle of the sequence.
d = 50
mu = 2
sigma = 0.7
tau = 35
n = 50
set.seed(1)
y = rbind(matrix(rnorm(d*tau),tau), matrix(rnorm(d*(n-tau),mu/sqrt(d),sigma), n-tau))
K = gaussiankernel(y)
a = kerseg1(n, K, pval.perm=TRUE, B=1000)