Simultaneous Detection and Localization of Mean and Covariance Changes in High Dimensions

TL;DR

This paper introduces a new method for detecting and localizing simultaneous changes in mean and covariance in high-dimensional data, improving accuracy over existing separate approaches.

Contribution

It proposes a joint monitoring approach with asymptotic independence, enabling combined p-value testing and adaptive localization in high-dimensional changepoint detection.

Findings

The joint test converges to a bivariate normal distribution.

The method outperforms existing techniques in simulations.

It achieves higher detection power and localization accuracy.

Abstract

Existing methods for high-dimensional changepoint detection and localization typically focus on changes in either the mean vector or the covariance matrix separately. This separation reduces detection power and localization accuracy when both parameters change simultaneously. We propose a simple yet powerful method that jointly monitors shifts in both the mean and covariance structures. Under mild conditions, the test statistics for detecting these shifts jointly converge in distribution to a bivariate standard normal distribution, revealing their asymptotic independence. This independence enables the combination of the individual p-values using Fisher's method, and the development of an adaptive p-value-based estimator for the changepoint. Theoretical analysis and extensive simulations demonstrate the superior performance of our method in terms of both detection power and localization accuracy.