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

arXiv: https://arxiv.org/abs/2511.19960 · HTML: https://mlsanity.com/paper/2511.19960/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2025.

## Built on by (most cited first, 1 of 1)

- [The Benjamini--Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests](https://mlsanity.com/paper/2607.12208/) (2026)

## Abstract (arXiv)

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.