Some Asymptotic Results on Multiple Testing under Weak Dependence

TL;DR

This paper analyzes the asymptotic behavior of multiple testing procedures like Bonferroni and Sidak under weak dependence, demonstrating their exact FWER control as the number of hypotheses grows large, with supporting simulations.

Contribution

It provides the first asymptotic results showing that Bonferroni and Sidak procedures control FWER exactly under weak dependence as hypotheses increase.

Findings

Bonferroni and Sidak control FWER asymptotically under weak dependence

Derived limiting results for generalized family-wise error rate and power

Simulation studies confirm asymptotic exactness of procedures

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.