WBSIP.cov {changepoints}

Wild binary segmentation for covariance change points detection through Independent Projection.

Description

Perform wild binary segmentation for covariance change points detection through Independent Projection

Usage

WBSIP.cov(X, X_prime, s, e, Alpha, Beta, delta, level = 0)

Arguments

X

A numeric vector of observations.

X_prime

A numeric vector of observations which are independent copy of X.

s

A integer scalar of starting index.

e

A integer scalar of ending index.

Alpha

A integer vector of starting indices of random intervals.

Beta

A integer vector of ending indices of random intervals.

delta

A positive integer scalar of minimum spacing.

level

A parameter for tracking the level at which a change point is detected. Should be fixed as 0.

Value

An object of class "BS", which is a list with the following structure:

S

A vector of estimated change points (sorted in strictly increasing order)

Dval

A vector of values of CUSUM statistic based on KS distance

Level

A vector representing the levels at which each change point is detected

Parent

A matrix with the starting indices on the first row and the ending indices on the second row

Author(s)

Haotian Xu

References

Wang, Yu and Rinaldo (2021) <doi:10.3150/20-BEJ1249>.

See Also

thresholdBS for obtain change points estimation.

Examples

p = 10
A1 = gen.cov.mat(p, 1, "equal")
A2 = gen.cov.mat(p, 3, "power")
A3 = A1
set.seed(1234)
X = cbind(t(MASS::mvrnorm(50, mu = rep(0, p), A1)), 
          t(MASS::mvrnorm(50, mu = rep(0, p), A2)), 
          t(MASS::mvrnorm(50, mu = rep(0, p), A3)))
X_prime = cbind(t(MASS::mvrnorm(50, mu = rep(0, p), A1)), 
                t(MASS::mvrnorm(50, mu = rep(0, p), A2)), 
                t(MASS::mvrnorm(50, mu = rep(0, p), A3)))
intervals = WBS.intervals(M = 120, lower = 1, upper = dim(X)[2])
temp = WBSIP.cov(X, X_prime, 1, dim(X)[2], intervals$Alpha, intervals$Beta, delta = 5)
tau = sqrt(p*log(ncol(X)))*1.5
sort(thresholdBS(temp, tau)$cpt_hat[,1])