Nonparametric Change-Point Detection and Inference for High-Dimensional Distributions

Abstract

High-dimensional distributions can change without altering means or covariances, while the number of affected coordinates is often unknown. We propose nonparametric procedures that address both challenges through standardized rank comparisons of marginal distributions. Sum and maximum scans target dense and sparse changes, and a Cauchy combination adapts to unknown sparsity. The procedures require no marginal moment assumptions and extend to multiple-change detection through wild binary segmentation. Under a weakly dependent Gaussian copula model, we establish asymptotic null distributions, asymptotic independence, detection consistency, and localization guarantees. Simulations demonstrate competitive performance for changes in shape and tails, including alternatives that preserve the first two moments. Applications to gene expression and sensor data illustrate the practical benefits of combining dense and sparse evidence.