Adaptable Regularized CCA Tests for Independence of High-Dimensional Random Vectors

2026-07-11

AI Summary

This study addresses the failure of conventional independence tests for high-dimensional random vectors when the dimensionality exceeds the sample size. To overcome this limitation, the authors integrate ridge regularization and principal component dimension reduction into a canonical correlation analysis framework, yielding a stable testing procedure tailored to high-dimensional settings. They develop two test statistics based on the regularized likelihood ratio and the largest canonical correlation root, respectively. A novel data-driven, adaptive strategy is proposed for selecting the regularization parameter, and the asymptotic distributions of the test statistics are rigorously established under both the null and standard local alternative hypotheses. Extensive simulations demonstrate that the proposed method exhibits superior finite-sample performance across a variety of high-dimensional scenarios.

Abstract

We propose an adaptable testing procedure for independence between two high-dimensional random vectors. The method incorporates ridge regularization and principal component-based dimension reduction into the canonical correlation analysis (CCA) framework, thereby stabilizing classical test statistics in high-dimensional settings. Depending on the reduced dimension, we develop both a regularized likelihood ratio test and a regularized largest-root test to accommodate different testing scenarios. We establish the asymptotic behavior of the proposed procedures under both the null hypothesis and representative alternatives, and further develop a data-driven method for selecting the regularization parameter. Extensive simulation studies demonstrate favorable finite-sample performance across a broad range of settings.

Problem

• high-dimensional
• independence test
• canonical correlation analysis
• random vectors
• regularization

Innovation

• regularized CCA
• high-dimensional independence test
• ridge regularization
• principal component reduction
• data-driven parameter selection