CHANGE-POINT INFERENCE IN HIGH-DIMENSIONAL REGRESSION MODELS UNDER TEMPORAL DEPENDENCE

• 成果类型: Article
• 署名作者: Xu, Haotian; Wang, Daren; Zhao, Zifeng; Yu, Yi
• 署名单位: University of Warwick; University of Notre Dame; University of Notre Dame
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2380
• 发表日期: 2024
• 页码: 999-1026
• 关键词: lasso

摘要

This paper concerns the limiting distributions of change-point estimators, in a high-dimensional linear regression time-series context, where a regression object (y(t), X-t) is an element of R x R-p is observed at every time point t is an element of{1 , ... , n}. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in l(2)-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)).