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Optimal sequential detection by sparsity likelihood

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  • Huang, Jingyan
  • Chan, Hock Peng

Abstract

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.

Suggested Citation

  • Huang, Jingyan & Chan, Hock Peng, 2025. "Optimal sequential detection by sparsity likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:csdana:v:203:y:2025:i:c:s0167947324001737
    DOI: 10.1016/j.csda.2024.108089
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    References listed on IDEAS

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    1. Yudong Chen & Tengyao Wang & Richard J. Samworth, 2022. "High‐dimensional, multiscale online changepoint detection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 234-266, February.
    2. Chen, Yudong & Wang, Tengyao & Samworth, Richard J., 2022. "High-dimensional, multiscale online changepoint detection," LSE Research Online Documents on Economics 113665, London School of Economics and Political Science, LSE Library.
    3. Y. Mei, 2010. "Efficient scalable schemes for monitoring a large number of data streams," Biometrika, Biometrika Trust, vol. 97(2), pages 419-433.
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