Efficient Global Monitoring Statistics for High-Dimensional Data

TL;DR

This paper introduces a new class of global monitoring statistics for high-dimensional data streams that are flexible, easy to compute, and effective across various abnormal scenarios, improving upon existing methods.

Contribution

The authors develop a novel global monitoring statistic leveraging quantile information, applicable under flexible models and compatible with any suitable local monitoring statistic.

Findings

Perform well across diverse settings

Compare favorably with existing methods

Effective for various abnormal scenarios

Abstract

Global monitoring statistics play an important role for developing efficient monitoring schemes for high-dimensional data streams. A number of global monitoring statistics have been proposed in the literature. However, most of them only work for certain types of abnormal scenarios under specific model assumptions. How to develop global monitoring statistics that are powerful for any abnormal scenarios under flexible model assumptions is a long-standing problem in the statistical process monitoring field. To provide a potential solution to this problem, we propose a novel class of global monitoring statistics by making use of the quantile information in the underlying distribution of the local monitoring statistic. Our proposed global monitoring statistics are easy to calculate and can work under flexible model assumptions since they can be built on any local monitoring statistic that is suitable for monitoring a single data stream. Our simulation studies show that the proposed global monitoring statistics perform well across a broad range of settings, and compare favorably with existing methods.