Sequential Detection of Common Change in High-dimensional Data Stream

TL;DR

This paper develops an optimal multivariate EWMA chart for detecting common changes in high-dimensional data streams, comparing its performance with other methods and proposing threshold-based variants for sparse signals.

Contribution

It introduces an optimal weight design for multivariate EWMA charts and proposes threshold-based variants for sparse signal detection, with comprehensive performance comparisons.

Findings

EWMA chart with optimal weights outperforms other methods in detection delay

Threshold-based EWMA charts effectively detect sparse signals

EWMA procedure offers robust performance and easy design

Abstract

After obtaining an accurate approximation for $ARL_0$, we first consider the optimal design of weight parameter for a multivariate EWMA chart that minimizes the stationary average delay detection time (SADDT). Comparisons with moving average (MA), CUSUM, generalized likelihood ratio test (GLRT), and Shiryayev-Roberts (S-R) charts after obtaining their $ARL_0$ and SADDT's are conducted numerically. To detect the change with sparse signals, hard-threshold and soft-threshold EWMA charts are proposed. Comparisons with other charts including adaptive techniques show that the EWMA procedure should be recommended for its robust performance and easy design.