ADAPTIVE CHANGE POINT MONITORING FOR HIGH-DIMENSIONAL DATA

Teng Wu, Runmin Wang, Hao Yan, Xiaofeng Shao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we propose a class of monitoring statistics for a mean shift in a sequence of high-dimensional observations. Inspired by recent U-statistic based retrospective tests, we extend 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 existing methods in retrospective testing that use self-normalization, we introduce a class of estimators for the 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 advantages of the proposed methodology are demonstrated using simulation studies and real-data illustrations.

Original languageEnglish (US)
Pages (from-to)1583-1610
Number of pages28
JournalStatistica Sinica
Volume32
Issue number3
DOIs
StatePublished - Jul 2022

Keywords

  • Change point detection
  • U-statistics
  • sequential monitoring
  • sequential testing

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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