CI.regression {changepoints}

Confidence interval construction of change points for regression settings with change points.

Description

Construct element-wise confidence interval for change points.

Usage

CI.regression(
  cpt_init,
  cpt_LR,
  beta_hat,
  y,
  X,
  w = 0.9,
  B = 1000,
  M,
  alpha_vec,
  rounding = TRUE
)

Arguments

cpt_init

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

cpt_LR

An integer vector of refined 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.

B

An integer scalar corresponding to the number of simulated two-sided Brownian motion with drift.

M

An integer scalar corresponding to the length for each side of the limiting distribution, i.e. the two-sided Brownian motion with drift.

alpha_vec

An numeric vector in (0,1) representing the vector of significance levels.

rounding

A boolean scalar representing if the confidence intervals need to be rounded into integer intervals.

Value

An length(cpt_init)-2-length(alpha_vec) array of confidence 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$beta_hat[min_idx[1], min_idx[2]]), ncol = length(cpt_init)+1)
cpt_LR = local.refine.DPDU.regression(cpt_init, beta_hat, data$y, data$X, w = 0.9)
alpha_vec = c(0.01, 0.05, 0.1)
CI.regression(cpt_init, cpt_LR, beta_hat, data$y, data$X, w = 0.9, B = 1000, M = n, alpha_vec)