Abstract
This paper considers the problem of testing and estimation of change point where signals after the change point can be highly irregular, which departs from the existing literature that assumes signals after the change point to be piecewise constant or vary smoothly. A two-step approach is proposed to effectively estimate the location of the change point. The first step consists of a preliminary estimation of the change point that allows us to obtain unknown parameters for the second step. In the second step, we use a new procedure to determine the position of the change point. We show that, under suitable conditions, the desirable rate of convergence of the estimated change point can be obtained. We apply our method to analyze the Baidu search index of COVID-19 related symptoms and find December 8, 2019, to be the starting date of the COVID-19 pandemic.
Funding Statement
This research is partially supported by NSF Grants DMS-2311249 and NSF DMS-2027723.
Acknowledgments
The authors would like to thank the Associate Editor and the three reviewers for their constructive comments that helped to improve the paper.
Citation
Tobias Kley. Yuhan Philip Liu. Hongyuan Cao. Wei Biao Wu. "Change-point analysis with irregular signals." Ann. Statist. 52 (6) 2913 - 2930, December 2024. https://doi.org/10.1214/24-AOS2451
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