kerSeg {kerSeg}

New kernel-based change-point detection

Description

This package can be used to detect change-points where the distributions abruptly change. The Gaussian kernel with the median heuristic, which is the median of all pairwise distances among observations, is used.

Details

To compute the Gaussian kernel matrix with the median heuristic bandwidth, the function gaussiankernel should be used. The main functions are kerseg1 for the single change-point alternative and kerseg2 for the changed-interval alternative.

Author(s)

Hoseung Song and Hao Chen

Maintainer: Hoseung Song ([e-mail])

References

Song, H. and Chen, H. (2022). New kernel-based change-point detection. arXiv:2206.01853

See Also

kerseg1, kerseg2, gaussiankernel

Examples

## Sequence 1: change in the mean in the middle of the sequence.
d = 50
mu = 2
tau = 15
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)

## 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)