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

2025-11-25

AI Summary

In multiple testing of two-sided Gaussian means, conventional false discovery rate (FDR) procedures—such as the Benjamini–Hochberg (BH) method—fail to control FDR under arbitrary dependence, especially in two-sided settings where dependence structures violate standard assumptions. Method: This paper proposes the first dependency-robust FDR control framework for two-sided tests. It introduces the novel concept of “positive left-tail dependence under the null” (PLTDN), generalizing classical one-sided dependence assumptions to the two-sided case. Based on PLTDN, we construct a family of generalized shift-BH procedures, adaptable to arbitrary covariance structures via p-value adjustment. Contribution/Results: We prove that the proposed method strictly controls FDR under PLTDN. Extensive simulations and analysis of HIV gene expression data demonstrate that, while maintaining FDR ≤ α, it achieves substantially higher statistical power than standard BH—particularly in high-dimensional, strongly correlated settings.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Extending FDR control to correlated two-sided Gaussian mean tests
• Developing dependence-aware methods for valid false discovery rate control
• Proposing adjusted p-value procedures that incorporate correlation information

Innovation

• Extends PLTDN concept for two-sided Gaussian testing
• Proposes GSBH methods with p-value adjustments
• Incorporates correlation information for FDR control