Computationally efficient and data-adaptive change-point inference in high dimension

High-dimensional change-point inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive change-point testing. The key observation is that two statistics based on aggregating cumulative sum statistics over all dimensions and possible change-points 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 component wise 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.