Adaptive Change Point Monitoring for High-Dimensional Data
Adaptive Change Point Monitoring for High-Dimensional Data
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DOI：
10.5705/ss.202020.0438
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发表时间：
2021-01
影响因子：
1.4
通讯作者：
Teng Wu;Runmin Wang;Hao Yan;Xiaofeng Shao
中科院分区：
文献类型：
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作者：
Teng Wu;Runmin Wang;Hao Yan;Xiaofeng Shao
在本文中，我们提出了一类高维观测序列均值漂移的监测统计量。受Wang等人(2019)和Zhang等人(2020)最近发展的基于U-统计量的回溯检验的启发，我们提出了基于U-统计量的序贯监测方法，开发了一种新的自适应监测方法，可以实时检测密集和稀疏变化。与Wang等人(2019)和Zhang等人(2020)在检验中使用自归一化不同，我们引入了协方差矩阵的$q$-范数的一类估计量，并证明了它们的比率相合性。为了便于快速计算，我们进一步开发了递归算法来提高监测程序的计算效率。通过仿真研究和实际数据说明了该方法的优越性。
In this paper, we propose a class of monitoring statistics for a mean shift in a sequence of high-dimensional observations. Inspired by the recent U-statistic based retrospective tests developed by Wang et al.(2019) and Zhang et al.(2020), we advance the U-statistic based approach to the sequential monitoring problem by developing a new adaptive monitoring procedure that can detect both dense and sparse changes in real-time. Unlike Wang et al.(2019) and Zhang et al.(2020), where self-normalization was used in their tests, we instead introduce a class of estimators for $q$-norm of the covariance matrix and prove their ratio consistency. To facilitate fast computation, we further develop recursive algorithms to improve the computational efficiency of the monitoring procedure. The advantage of the proposed methodology is demonstrated via simulation studies and real data illustrations.