LRV.regression {changepoints}

Long-run variance estimation for regression settings with change points.

Description

Estimating long-run variance for regression settings with change points.

Usage

LRV.regression(cpt_init, beta_hat, y, X, w = 0.9, block_size)

Arguments

cpt_init

An integer vector of initial changepoints estimation (sorted in strictly increasing order).

beta_hat

A numeric (px(K_hat+1))matrix of estimated regression coefficients.

y

A numeric vector of response variable.

X

A numeric matrix of covariates with vertical axis being time.

w

A numeric scalar in (0,1) representing the weight for interval truncation.

block_size

An integer scalar corresponding to the block size S in the paper.

Value

A vector of long-run variance estimators associated with all local refined intervals.

Author(s)

Haotian Xu

References

Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.

Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.

Examples

d0 = 5
p = 10
n = 200
cpt_true = c(70, 140)
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)
lambda_set = c(0.1, 0.5, 1, 2)
zeta_set = c(10, 15, 20)
temp = CV.search.DPDU.regression(y = data$y, X = data$X, lambda_set, zeta_set)
temp$test_error # test error result
# find the indices of lambda_set and zeta_set which minimizes the test error
min_idx = as.vector(arrayInd(which.min(temp$test_error), dim(temp$test_error))) 
lambda_set[min_idx[2]]
zeta_set[min_idx[1]]
cpt_init = unlist(temp$cpt_hat[min_idx[1], min_idx[2]])
beta_hat = matrix(unlist(temp$beta_hat[min_idx[1], min_idx[2]]), ncol = length(cpt_init)+1)
interval_refine = trim_interval(n, cpt_init)
# choose S
block_size = ceiling(sqrt(min(floor(interval_refine[,2]) - ceiling(interval_refine[,1])))/2)
LRV_est = LRV.regression(cpt_init, beta_hat, data$y, data$X, w = 0.9, block_size)