Open Access
2023 Change-point inference for high-dimensional heteroscedastic data
Teng Wu, Stanislav Volgushev, Xiaofeng Shao
Author Affiliations +
Electron. J. Statist. 17(2): 3893-3941 (2023). DOI: 10.1214/23-EJS2185


We propose a bootstrap-based test to detect a mean shift in a sequence of high-dimensional observations with unknown time-varying heteroscedasticity. The proposed test builds on the U-statistic based approach in Wang et al. (2022), targets a dense alternative, and adopts a wild bootstrap procedure to generate critical values. The bootstrap-based test is free of tuning parameters and is capable of accommodating unconditional time varying heteroscedasticity in the high-dimensional observations, as demonstrated in our theory and simulations. Theoretically, we justify the bootstrap consistency by using the recently proposed unconditional approach in Bücher and Kojadinovic (2019). Extensions to testing for multiple change-points and estimation using wild binary segmentation are also presented. Numerical simulations demonstrate the robustness of the proposed testing and estimation procedures with respect to different kinds of time-varying heteroscedasticity.

Funding Statement

Stanislav Volgushev was supported by a grant from NSERC of Canada; Xiaofeng Shao was supported by grants NSF-DMS2014018 and NSF-DMS2210002.


We would like to thank two referees for constructive comments, which led to substantial improvements.


Download Citation

Teng Wu. Stanislav Volgushev. Xiaofeng Shao. "Change-point inference for high-dimensional heteroscedastic data." Electron. J. Statist. 17 (2) 3893 - 3941, 2023.


Received: 1 July 2022; Published: 2023
First available in Project Euclid: 11 December 2023

arXiv: 2311.09419
Digital Object Identifier: 10.1214/23-EJS2185

Primary: 62F40 , 62H15
Secondary: 62G10 , 62G20

Keywords: bootstrap , dense alternative , U-statistic

Vol.17 • No. 2 • 2023
Back to Top