Abstract

This paper addresses the challenge of detecting the change point in the covariance matrix of

a high-dimensional random vector sequence. A novel reweighted CUSUM-type statistic is introduced,

incorporating a data-adaptive parameter selection method to optimize weight determination. Building

on this statistic, we develop a comprehensive framework for change point detection. Additionally,

a hypothesis testing procedure is proposed to assess the existence of the change point based on

our methodology.

The study provides rigorous theoretical foundations for the proposed method,

demonstrating the validity of parameter selection and the consistency of change point estimation. The

effectiveness of the method is substantiated through extensive simulation studies and real-world data

analysis, confirming its practical applicability and statistical reliability.

Information

Preprint No.SS-2025-0327
Manuscript IDSS-2025-0327
Complete AuthorsCanhuang Xu, Lei Shu, Yu Chen, Qing Yang
Corresponding AuthorsYu Chen
Emailscyu@ustc.edu.cn

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Acknowledgments

The authors are grateful to the editor, associate editor, and reviewers for their insightful comments and suggestions, which have improved the article significantly. The work is supported

by the National Natural Science Foundation of China (Nos. 12371279, 12501391,12571297,

12231017), National Key R&D Program of China-2022YFA1008000, and the CAS Talent

Introduction Program (Category B). Canhuang Xu and Lei Shu are co-first authors.

Supplementary Materials

The supplementary material contains some lemmas that are essential for our proofs, as well

as the proofs of the theorem and proposition introduced in Section 3.

Supplementary materials are available for download.