Computationally efficient and data-adaptive changepoint inference in high dimension

Abstract

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 asymptotic null distributions. To this end, we develop new tools and techniques to establish the asymptotic distribution of the maximum-type statistic under a more relaxed condition on componentwise correlations among all variables than those in existing literature. The proposed method is simple to use. It is adaptive to different levels of the sparsity of change signals, and is comparable to or even outperforms existing approaches as revealed by our numerical studies.