Asymptotic control of FWER under Gaussian assumption: application to correlation tests

TL;DR

This paper develops a unified asymptotic framework for multiple testing correction procedures under Gaussian assumptions, particularly for correlation tests, ensuring FWER control even with highly correlated tests, and validates the methods through simulations and real data.

Contribution

It introduces a unified approach to analyze asymptotic behavior of multiple correction procedures for Gaussian statistics, extending their validity to highly correlated tests.

Findings

FWER is controlled in correlation tests under the proposed framework.

Simulation studies show robustness across different graph sparsity levels.

Real data application confirms the practical effectiveness of the methods.

Abstract

In many applications, hypothesis testing is based on an asymptotic distribution of statistics. The aim of this paper is to clarify and extend multiple correction procedures when the statistics are asymptotically Gaussian. We propose a unified framework to prove their asymptotic behavior which is valid in the case of highly correlated tests. We focus on correlation tests where several test statistics are proposed. All these multiple testing procedures on correlations are shown to control FWER. An extensive simulation study on correlation-based graph estimation highlights finite sample behavior, independence on the sparsity of graphs and dependence on the values of correlations. Empirical evaluation of power provides comparisons of the proposed methods. Finally validation of our procedures is proposed on real dataset of rats brain connectivity measured by fMRI. We confirm our theoretical findings by applying our procedures on a full null hypotheses with data from dead rats. Data on alive rats show the performance of the proposed procedures to correctly identify brain connectivity graphs with controlled errors.