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arXiv · 2511.19960

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

Deepra Ghosh·Sanat K. Sarkar
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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.

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Deepra Ghosh, Sanat K. Sarkar. 2025-11-25. Dependence-Aware False Discovery Rate Control in Two-Sided Gaussian Mean Testing. https://arxiv.org/abs/2511.19960

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