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 they 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.

翻译：我们证明两种错误发现率（FDR）控制方法——针对相依p值的Benjamini-Yekutieli方法以及针对相依e值的e-Benjamini-Hochberg方法——均可通过引入一个独立均匀随机变量的简单随机化步骤显著提升效能。作为推论，任意相依条件下的Hommel检验也得到改进。重要的是，我们提出的随机化改进方案不会劣于原始方法，且在仿真实验中展现出更严格的统计优势，效能提升效果显著。该技术同样可推广至几乎所有基于e值的多重检验方法。