On High-Dimensional Change-Point Detection Based on Pairwise Distances

Abstract: In change-point analysis, one aims at finding the locations of abrupt distributional changes (if any) in a sequence of multivariate observations. In this article, we propose some nonparametric methods based on averages of pairwise distances for this purpose. These distance-based methods can be conveniently used for high-dimensional data even when the dimension is much larger than the sample size (i.e., the length of the sequence). We carry out some theoretical investigations on the behaviour of these methods not only when the dimension of the data remains fixed and the sample size grows to infinity, but also in situations where the dimension diverges to infinity while the sample size may or may not grow with the dimension. Several high-dimensional datasets are analyzed to compare the empirical performance of these proposed methods against some state-of-the-art methods.