Adaptive Change Point Monitoring for High-Dimensional Data

TL;DR

This paper introduces an adaptive sequential monitoring method for high-dimensional data that effectively detects both dense and sparse mean shifts in real-time, improving computational efficiency and accuracy over previous approaches.

Contribution

It advances U-statistic based sequential monitoring by developing adaptive procedures with ratio-consistent covariance estimators and recursive algorithms for faster computation.

Findings

Effective detection of mean shifts in high-dimensional data

Improved computational efficiency through recursive algorithms

Validated performance via simulations and real data

Abstract

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.