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.

翻译：我们证明，两种针对错误发现率控制的方法——适用于依赖p值的Benjamini-Yekutieli方法，以及适用于依赖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过程获得更强效力。作为推论，任意依赖条件下的Hommel检验也得到改进。重要的是，我们的随机化改进方案的表现始终不劣于原始方法，且在模拟实验中通常具有显著提升的严格统计效力。该技术同样能有效改进几乎所有基于e值的其他多重检验方法。