Detection and inference of changes in high-dimensional linear regression with nonsparse structures

• 成果类型: Article; Early Access
• 署名作者: Cho, Haeran; Kley, Tobias; Li, Housen
• 署名单位: University of Bristol; University of Gottingen
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf029
• 发表日期: 2025
• 关键词: confidence-intervals; SPARSE; Lasso; models; segmentation; rates

摘要

For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be exactly sparse segment-wise, which enables many existing methods to estimate the parameters locally via & ell;1-regularized maximum-likelihood-type estimation and then contrast them for change point detection. Contrary to this common practice, we show that the exact sparsity of neither regression parameters nor their differences, a.k.a. differential parameters, is necessary for consistency in multiple change point detection. In fact, both statistically and computationally, better efficiency is attained by a simple strategy that scans for large discrepancies in local covariance between the regressors and the response. We go a step further and propose a suite of tools for directly inferring about the differential parameters post-segmentation, which are applicable even when the regression parameters themselves are nonsparse. Theoretical investigations are conducted under general conditions permitting non-Gaussianity, temporal dependence, and ultra-high dimensionality. Numerical results from simulated and macroeconomic datasets demonstrate the competitiveness and efficacy of the proposed methods. Implementation of all methods is provided in the R package inferchange on GitHub.