An Asymptotically Exact Multiple Testing Procedure under Dependence

TL;DR

This paper introduces a simple, asymptotically exact single-step multiple testing procedure for dependent Gaussian data that controls the family-wise error rate precisely, with demonstrated theoretical guarantees and simulation validation.

Contribution

It presents a novel single-step testing method that asymptotically controls FWER under dependence without stepwise adjustments, extending to block correlations and generalized FWER.

Findings

Controls FWER exactly asymptotically

Effective under equicorrelated Gaussian models

Extensible to block-dependent structures

Abstract

We propose a simple single-step multiple testing procedure that asymptotically controls the family-wise error rate (FWER) at the desired level exactly under the equicorrelated multivariate Gaussian setup. The method is shown to be asymptotically exact using an explicit plug-in estimator for the equicorrelation, and does not require stepwise adjustments. We establish its theoretical properties, including the convergence to the desired error level, and demonstrate its effectiveness through simulation results. We also spell out related extensions to block-correlated structures and generalized FWER control.