Adaptive L-tests for high dimensional independence

2026-01-27

AI Summary

This study addresses the challenge of testing mutual independence among multiple variables in high-dimensional settings by proposing an adaptive test based on L-statistics. The method leverages a novel theoretical result establishing the asymptotic independence between fixed-order and diverging-order L-statistics, which are then combined via the Cauchy combination method to construct a test statistic that enjoys both strong theoretical guarantees and broad power across diverse alternative hypotheses. By effectively integrating high-dimensional statistical inference with asymptotic distribution theory, the proposed approach demonstrates superior empirical power. Extensive simulations confirm its robust performance and significantly improved efficacy compared to existing methods.

Technology Category

• Machine Learning: Statistical Relational/Logic Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual independence based on $L$-statistics. We establish the asymptotic distribution of the proposed test when the order parameter $k$ is fixed, and prove asymptotic normality when $k$ diverges with the dimension. Moreover, we show the asymptotic independence of the fixed-$k$ and diverging-$k$ statistics, enabling their combination through the Cauchy method. The resulting adaptive test is both theoretically justified and practically powerful across a wide range of alternatives. Simulation studies demonstrate the advantages of our method.

Problem

• high-dimensional independence
• mutual independence
• L-statistics
• adaptive testing
• asymptotic distribution

Innovation

• L-statistics
• high-dimensional independence
• adaptive testing
• asymptotic normality
• Cauchy combination