Change-point inference in high-dimensional regression models under temporal dependence
Haotian Xu, Daren Wang, Zifeng Zhao, Yi Yu
The Annals of Statistics · 2024 · Volume 52 · Issue 3
Abstract
This paper concerns the limiting distributions of change-point estimators, in a high-dimensional linear regression time-series context, where a regression object (yt,Xt)∈R×Rp is observed at every time point t∈{1,…,n}. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in ℓ2-norm. We provide limiting distributions of the change-point estimators in the regimes where the minimal jump size vanishes and where it remains a constant. We allow for both the covariate and noise sequences to be temporally dependent, in the functional dependence framework, which is the first time seen in the change-point inference literature. We show that a block-type long-run variance estimator is consistent under the functional dependence, which facilitates the practical implementation of our derived limiting distributions. We also present a few important byproducts of our analysis, which are of their own interest. These include a novel variant of the dynamic programming algorithm to boost the computational efficiency, consistent change-point localization rates under temporal dependence and a new Bernstein inequality for data possessing functional dependence. Extensive numerical results are provided to support our theoretical results. The proposed methods are implemented in the R package changepoints (Xu et al. (2022)).
Keywords
62F30, 62F35, Change-point inference, Confidence interval, high-dimensional linear regression, long-run variance, temporal dependence
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