Dependence-Aware False Discovery Rate Control in Two-Sided Gaussian Mean Testing

TL;DR

This paper introduces a new framework for controlling the false discovery rate in two-sided Gaussian mean tests under dependence, extending classical assumptions and proposing generalized methods that improve power and reliability.

Contribution

It extends FDR control theory to two-sided tests with dependence by defining PLTDN and proposes GSBH methods that incorporate correlation adjustments.

Findings

GSBH methods achieve reliable FDR control under dependence.

Simulation studies show improved power over traditional BH procedures.

Application to HIV data demonstrates practical effectiveness.

Abstract

This paper develops a general framework for controlling the false discovery rate (FDR) in multiple testing of Gaussian means against two-sided alternatives. The widely used Benjamini-Hochberg (BH) procedure provides exact FDR control under independence or conservative control under specific one-sided dependence structures, but its validity for correlated two-sided tests has remained an open question. We introduce the notion of positive left-tail dependence under the null (PLTDN), extending classical dependence assumptions to two-sided settings, and show that it ensures valid FDR control for BH-type procedures. Building on this framework, we propose a family of generalized shifted BH (GSBH) methods that incorporate correlation information through simple p-value adjustments. Simulation results demonstrate reliable FDR control and improved power across a range of dependence structures, while an application to an HIV gene expression dataset illustrates the practical effectiveness of the proposed approach.