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

2026-09-13

AI Summary

本文提出非参数方法，通过标准化秩比较解决高维分布变化点检测问题，适用于未知稀疏性情况，无需边际矩假设。

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.

Problem

• Nonparametric
• Change-Point Detection
• High-Dimensional Distributions
• Marginal Distributions
• Sparsity

Innovation

• nonparametric procedures
• standardized rank comparisons
• Cauchy combination
• wild binary segmentation
• high-dimensional distributions