kerseg2 {kerSeg}

Kernel-based change-point detection for changed-interval alternatives

Description

This function finds an interval in the sequence where their underlying distribution differs from the rest of the sequence.

Usage

kerseg2(n, K, r1=1.2, r2=0.8, l0=0.05*n, l1=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_{1},t_{2}).

r2

The constant in the test statistics \textrm{Z}_{W,r2}(t_{1},t_{2}).

l0

The minimum length of the interval to be considered as a changed interval.

l1

The maximum length of the interval to be considered as a changed interval.

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 changed-interval, 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 matrix of each scan statistic (standardized counts).

Zmax

The test statistics (maximum of the scan statistics).

tauhat

An estimate of the two ends of the changed-interval.

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, kerseg2, gaussiankernel, kerseg1

Examples

## Sequence 3: change in both the mean and variance happens on an interval.
d = 50
mu = 2
sigma = 0.5
tau1 = 25
tau2 = 35
n = 50
set.seed(1)
y1 = matrix(rnorm(d*tau1),tau1)
y2 = matrix(rnorm(d*(tau2-tau1),mu/sqrt(d),sigma), tau2-tau1)
y3 = matrix(rnorm(d*(n-tau2)), n-tau2)
y = rbind(y1, y2, y3)
K = gaussiankernel(y)
a = kerseg2(n, K, pval.perm=TRUE, B=1000)