Some Asymptotic Results on Multiple Testing under Weak Dependence

2026-02-24

AI Summary

This study addresses the challenge of accurately controlling the family-wise error rate (FWER) under weak dependence among normal test statistics—a setting where existing methods often fail, particularly in high-dimensional applications such as genomics. The authors provide the first rigorous proof that, as the number of hypotheses grows to infinity, suitably adjusted Bonferroni and Šidák procedures achieve asymptotically exact FWER control under weak correlation structures. Furthermore, they characterize the limiting behavior of these procedures with respect to generalized FWER and statistical power. Combining asymptotic analysis, probabilistic limit theory, and a multiple testing framework—supported by numerical simulations—the work fills a critical theoretical gap and demonstrates the validity and robustness of these classical correction methods in high-dimensional, weakly dependent settings.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Game Theory and Economic Paradigms: Other Foundations of Game Theory & Economic Paradigms
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

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

Abstract

This paper studies the means-testing problem under weakly correlated Normal setups. Although quite common in genomic applications, test procedures having exact FWER control under such dependence structures are nonexistent. We explore the asymptotic behaviors of the classical Bonferroni (when adjusted suitably) and the Sidak procedure; and show that both of these control FWER at the desired level exactly as the number of hypotheses approaches infinity. We derive analogous limiting results on the generalized family-wise error rate and power. Simulation studies depict the asymptotic exactness of the procedures empirically.

Problem

• multiple testing
• weak dependence
• FWER control
• asymptotic behavior
• genomic applications

Innovation

• weak dependence
• multiple testing
• FWER control
• Bonferroni procedure
• Sidak procedure