changepoints (version 1.1.0)

simu.change.regression: Simulate a sparse regression model with change points in coefficients.

Description

Simulate a sparse regression model with change points in coefficients under temporal dependence.

Usage

simu.change.regression(
  d0,
  cpt_true,
  p,
  n,
  sigma,
  kappa,
  cov_type = "I",
  mod_X = "IID",
  mod_e = "IID"
)

Value

A list with the following structure:

cpt_true

A vector of true changepoints (sorted in strictly increasing order).

X

An n-by-p design matrix.

y

An n-dim vector of response variable.

betafullmat

A p-by-n matrix of coefficients.

Arguments

d0

A numeric scalar stands for the number of nonzero coefficients.

cpt_true

An integer vector contains true change points (sorted in strictly increasing order).

p

An integer scalar stands for the dimensionality.

n

An integer scalar stands for the sample size.

sigma

A numeric scalar stands for error standard deviation.

kappa

A numeric scalar stands for the minimum jump size of coefficient vector in \(l_2\) norm.

cov_type

A character string stands for the type of covariance matrix of covariates. 'I': Identity; 'T': Toeplitz; 'E': Equal-correlation.

mod_X

A character string stands for the time series model followed by the covariates. 'IID': IID multivariate Gaussian; 'AR': Multivariate AR1 with rho = 0.3; Multivariate MA1 theta = 0.3.

mod_e

A character string stands for the time series model followed by the errors 'IID': IID univariate Gaussian; 'AR': Univariate AR1 with rho = 0.3; Univariate MA1 theta = 0.3.

Author

Daren Wang, Zifeng Zhao & Haotian Xu

References

Rinaldo, Wang, Wen, Willett and Yu (2020) <arxiv:2010.10410>; Xu, Wang, Zhao and Yu (2022) <arXiv:2207.12453>.

Examples

d0 = 10
p = 30
n = 100
cpt_true = c(10, 30, 40, 70, 90)
data = simu.change.regression(d0, cpt_true, p, n, sigma = 1, kappa = 9)