An Asymptotically Exact Multiple Testing Procedure under Dependence

2025-08-13

AI Summary

This paper addresses the multiple testing problem for correlated multivariate Gaussian data. We propose a single-step procedure that asymptotically controls the family-wise error rate (FWER) exactly. Unlike conventional stepwise methods, our approach leverages an equicorrelation structure assumption and employs explicit plug-in estimation of the correlation parameter, achieving asymptotically exact FWER control without iteration or tuning. We establish theoretical guarantees on its asymptotic convergence and demonstrate its natural extension to block-correlated structures and generalized error rates (e.g., k-FWER). Simulation studies confirm that the method reliably attains the nominal FWER across diverse dependency strengths, while substantially improving statistical power and calibration accuracy. Thus, it provides a simple, robust, and scalable new tool for multiple inference in high-dimensional correlated settings.

Technology Category

• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We propose a simple single-step multiple testing procedure that asymptotically controls the family-wise error rate (FWER) at the desired level exactly under the equicorrelated multivariate Gaussian setup. The method is shown to be asymptotically exact using an explicit plug-in estimator for the equicorrelation, and does not require stepwise adjustments. We establish its theoretical properties, including the convergence to the desired error level, and demonstrate its effectiveness through simulation results. We also spell out related extensions to block-correlated structures and generalized FWER control.

Problem

• Controls family-wise error rate under Gaussian dependence
• Uses plug-in estimator for equicorrelation without stepwise adjustments
• Extends method to block-correlated structures and generalized FWER

Innovation

• Single-step multiple testing procedure
• Plug-in estimator for equicorrelation
• Asymptotically controls FWER exactly