Abstract

We propose a novel approach for detecting change points in high

dimensional linear regression models. Unlike previous research that relies on strict

Gaussian/sub-Gaussian error assumptions and has prior knowledge of change

points, we propose a tail-adaptive method for change point detection and estimation. We use a weighted combination of composite quantile and least squared

losses to build a new loss function, allowing us to leverage information from both

conditional means and quantiles. For change point testing, we develop a family

of individual testing statistics with different weights to account for unknown tail

structures. These individual tests are further aggregated to construct a powerful

tail-adaptive test for sparse regression coefficient changes. For change point estimation, we propose a family of argmax-based individual estimators. We provide

theoretical justifications for the validity of these tests and change point estimators. Additionally, we introduce a new algorithm for detecting multiple change

points in a tail-adaptive manner using the wild binary segmentation. Extensive

numerical results show the effectiveness of our proposed method.

Information

Preprint No.SS-2023-0337
Manuscript IDSS-2023-0337
Complete AuthorsBin Liu, Zhengling Qi, Xinsheng Zhang, Yufeng Liu
Corresponding AuthorsYufeng Liu
Emailsyfliu@email.unc.edu

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Acknowledgments

The authors are indebted to the editor, the associate editor, and two

referees, whose helpful comments and suggestions led to a much improved

presentation. Bin Liu was supported in part by the National Natural Science Foundation of China 12101132, 12331009.

Supplementary Materials

The online Supplementary Material provides detailed basic assumptions

and proofs of the main theory, and additional numerical results including

size, power, multiple change point detection. In addition, an interesting

application to the S&P100 data analysis is also provided.

Supplementary materials are available for download.