Behaviour of FWER in Normal Distributions

TL;DR

This paper investigates how the familywise error rate (FWER) behaves when using the Bonferroni correction in multiple testing scenarios involving normal distributions, providing bounds under various correlation structures.

Contribution

It establishes nonasymptotic upper bounds on FWER for the Bonferroni method in both equicorrelated and general normal models, advancing understanding of its error control properties.

Findings

Upper bounds on FWER under equicorrelated normal setup

Upper bounds on FWER in general normal setup

Insights into Bonferroni method's error control in normal distributions

Abstract

Familywise error rate (FWER) has been a cornerstone in simultaneous inference for decades, and the classical Bonferroni method has been one of the most prominent frequentist approaches for controlling FWER. The present article studies the behavior of the FWER for Bonferroni procedure in a multiple testing problem. We establish upper bounds on FWER for Bonferroni method under the equicorrelated and general normal setups in nonasymptotic case.