Adaptable High-Dimensional Change Point Detection via Ridge Regularization

2026-05-23

AI Summary

This study addresses the problem of multiple change-point detection in the mean vector of high-dimensional independent observation sequences, particularly when the dimensionality is comparable to the sample size. The authors propose a class of ridge-regularized CUSUM statistics based on a tunable ridge-regularized Hotelling’s T² test for detecting dense change points in high dimensions. By incorporating ridge regularization, the method achieves covariance-adaptive stabilization in normalization, enabling the derivation of asymptotic distribution theory for the proposed statistic. A principled framework for selecting the regularization parameter is developed to maximize asymptotic power. Numerical experiments demonstrate that the proposed approach substantially outperforms existing methods across various high-dimensional settings and successfully identifies change points in a panel of daily log returns of S&P 500 constituent stocks from 2007 to 2025.

Abstract

We study the problem of detecting multiple change points in the mean vectors of an independent sequence of high-dimensional observations. We propose a family of ridge-regularized CUSUM statistics built upon the adaptable ridge-regularized Hotelling's T2 test of Li et al. (Ann. Statist. 48 (2020) 1815-1847). The proposed tests are designed for dense alternatives in the high-dimensional regime where the dimension is comparable to the sample size. By introducing ridge regularization, the procedure achieves a stable form of sample covariance normalization and attains adaptability with respect to the underlying population covariance structure. We derive the limiting distributions of the proposed statistics under mild conditions, both under the null hypothesis and under a class of local alternatives. We further develop a principled framework for selecting the regularization parameter by maximizing asymptotic power. Extensive simulation studies demonstrate that the proposed tests compare favorably with a wide range of existing methods across diverse settings. The performance of the proposed test procedure is illustrated through an application to a panel of daily log-returns from S&P 500 constituents spanning 2007-2025.

Problem

• change point detection
• high-dimensional data
• mean vector
• multiple change points
• ridge regularization

Innovation

• ridge regularization
• high-dimensional change point detection
• CUSUM statistic
• adaptive covariance normalization
• asymptotic power