Computationally efficient and data-adaptive changepoint inference in high dimension

TL;DR

This paper introduces a fast, adaptive changepoint inference method for high-dimensional data that combines two asymptotically independent statistics, improving detection across various change patterns with computational efficiency.

Contribution

It proposes a novel, simple approach that combines maximum- and summation-type statistics for high-dimensional changepoint detection, with relaxed correlation conditions and improved adaptivity.

Findings

Method is computationally efficient and easy to implement.

Outperforms existing approaches in numerical studies.

Effective across different sparsity levels of change signals.

Abstract

High-dimensional changepoint inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive changepoint testing. The key observation is that two statistics based on aggregating cumulative sum statistics over all dimensions and possible changepoints by taking their maximum and summation, respectively, are asymptotically independent under some mild conditions. Hence we are able to form a new test by combining the p-values of the maximum- and summation-type statistics according to their limit null distributions. To this end, we develop new tools and techniques to establish asymptotic distribution of the maximum-type statistic under a more relaxed condition on componentwise correlations among all variables than that in existing literature. The proposed method is simple to use and computationally efficient. It is adaptive to different sparsity levels of change signals, and is comparable to or even outperforms existing approaches as revealed by our numerical studies.