Multiple change point detection for high-dimensional data

Wenbiao Zhao, Lixing Zhu () and Falong Tan ()
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Wenbiao Zhao: Beijing Institute of Technology
Lixing Zhu: Beijing Normal University at Zhuhai
Falong Tan: Hunan University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 33, issue 3, No 12, 809-846

Abstract: Abstract This research investigates the detection of multiple change points in high-dimensional data without particular sparse or dense structure, where the dimension can be of exponential order in relation to the sample size. The estimation approach proposed employs a signal statistic based on a sequence of signal screening-based local U-statistics. This technique avoids costly computations that exhaustive search algorithms require and mitigates false positives, which hypothesis testing-based methods need to control. Consistency of estimation can be achieved for both the locations and number of change points, even when the number of change points diverges at a certain rate as the sample size increases. Additionally, the visualization nature of the proposed approach makes plotting the signal statistic a useful tool to identify locations of change points, which distinguishes it from existing methods in the literature. Numerical studies are performed to evaluate the effectiveness of the proposed technique in finite sample scenarios, and a real data analysis is presented to illustrate its application.

Keywords: High-dimensional data; Multiple change points; Data screened local U-statistics; Ridge ratios; Visualization; 62F03 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11749-024-00926-w

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