Change-point detection in high-dimensional covariance structure

TL;DR

This paper presents a new high-dimensional covariance change-point detection method using a bootstrap-based testing procedure, suitable for online applications with proven theoretical guarantees and superior performance in simulations.

Contribution

Introduces a novel bootstrap-based testing approach for detecting covariance changes in high-dimensional data with theoretical validation and practical advantages.

Findings

Method controls false alarm probability effectively

High detection power demonstrated in simulations

Approach suitable for online change-point detection

Abstract

In this paper we introduce a novel approach for an important problem of break detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process -- a problem, which has applications in many areas e.g., neuroimaging and finance. The developed approach is essentially a testing procedure involving a choice of a critical level. To that end a non-standard bootstrap scheme is proposed and theoretically justified under mild assumptions. Theoretical study features a result providing guaranties for break detection. All the theoretical results are established in a high-dimensional setting (dimensionality $p \gg n$). Multiscale nature of the approach allows for a trade-off between sensitivity of break detection and localization. The approach can be naturally employed in an on-line setting. Simulation study demonstrates that the approach matches the nominal level of false alarm probability and exhibits high power, outperforming a recent approach.