Mingzhou Deng | Searcharxiv

arXiv2026

The Randomized BH Procedure: A Generalized Framework Encompassing Conformal and Competition Tests

We propose the Randomized BH procedure, a generalized framework that introduces randomization into the Benjamini-Hochberg (BH) procedure for false discovery rate (FDR) control. We show that the classical BH procedure as well as two recently developed families of null-distribution-free methods, competition tests and conformal tests, share a common theoretical foundation and arise as special cases of this framework. The Randomized BH relaxes the classical conditions required for FDR control, frees conformal tests from the strict exchangeability assumption while allowing calibration sets to be constructed via pre-screening, and enables competition tests to be analyzed through the well-developed theory of p-values. We illustrate the framework through two applications. The first is a deeper analysis of compound p-values through the lens of randomization. The second is a general approach for integrating distributed multiple testing problems while maintaining global FDR control. Numerical simulations confirm the validity of our theoretical results.

math.ST↗

arXiv2025

Grouped Competition Test with Unified False Discovery Rate Control

This paper discusses several p-value-free multiple hypothesis testing methods proposed in recent years and organizes them by introducing a unified framework termed competition test. Although existing competition tests are effective in controlling the False Discovery Rate (FDR), they struggle with handling data with strong heterogeneity or dependency structures. Based on this framework, the paper proposes a novel approach that applies a corrected competition procedure to group data with certain structure, and then integrates the results from each group. Using the favorable properties of competition test, the paper proposes a theorem demonstrating that this approach controls the global FDR. We further show that although the correction parameters may lead to a slight loss in power, such loss is typically minimal. Through simulation experiments and mass spectrometry data analysis, we illustrate the flexibility and efficacy of our approach.

stat.ME↗