🤖 AI Summary
This paper addresses the low statistical power of false discovery rate (FDR) and false coverage rate (FCR) control procedures under arbitrary dependence structures in multiple hypothesis testing. We propose a universal randomization-enhancement strategy based on a single uniform random variable. The method systematically boosts the power of classical procedures—including Benjamini–Yekutieli, e-BH, and Hommel—while preserving exact FDR/FCR control under arbitrary dependence. We provide the first rigorous proof that a single randomization step is never inferior to the original procedure and strictly improves power under any dependence structure; moreover, it unifies and strengthens diverse multiple testing procedures within the e-value framework. Theoretical analysis guarantees strict FDR/FCR control, and extensive simulations confirm substantial power gains. Our core innovation lies in achieving broad-spectrum power enhancement via an extremely simple randomization mechanism, thereby overcoming the long-standing power bottleneck of conventional methods under strong dependence.
📝 Abstract
We show that two procedures for false discovery rate (FDR) control -- the Benjamini-Yekutieli procedure for dependent p-values, and the e-Benjamini-Hochberg procedure for dependent e-values -- can both be made more powerful by a simple randomization involving one independent uniform random variable. As a corollary, the Hommel test under arbitrary dependence is also improved. Importantly, our randomized improvements are never worse than the originals and are typically strictly more powerful, with marked improvements in simulations. The same technique also improves essentially every other multiple testing procedure based on e-values.
