Optimal sequential detection by sparsity likelihood

We propose here a sparsity likelihood stopping rule to detect change-points when there are multiple data streams. It is optimal in the sense of minimizing, asymptotically, the detection delay when the change-points is present in only a small fraction of the data streams. This optimality holds at all...

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Bibliographic Details
Published in:Computational statistics & data analysis 2025-03, Vol.203, p.108089, Article 108089
Main Authors: Huang, Jingyan, Chan, Hock Peng
Format: Article
Language:English
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Summary:We propose here a sparsity likelihood stopping rule to detect change-points when there are multiple data streams. It is optimal in the sense of minimizing, asymptotically, the detection delay when the change-points is present in only a small fraction of the data streams. This optimality holds at all levels of change-point sparsity. A key contribution of this paper is that we show optimality when there is extreme sparsity. Extreme sparsity refers to the number of data streams with change-points increasing very slowly as the number of data streams goes to infinity. The theoretical results are backed by a numerical study that shows the sparsity likelihood stopping rule performing well at all levels of sparsity. Applications of the stopping rule on non-normal models are also illustrated here.
ISSN:0167-9473
DOI:10.1016/j.csda.2024.108089