AI 中文总结
该研究提出锚定技术，利用现有FDR证明的松弛性改进多重检验程序，得到的e-闭包透明保留基线发现并控制FDR，且在多种场景下优于对应基线程序。
AI 中文摘要
近期的e-闭包方法可恢复所有控制FDR（及其他期望损失）的程序，但恢复的e-集合具有“自指性”，无法为如何改进程序（若可改进）提供洞见，且近期一些改进略显不透明。我们引入一种名为锚定的基础新技术，该技术利用现有FDR证明中的松弛性，以扩大基线多重检验程序的自指局部e值。由此得到的e-闭包可透明保留所有基线发现（通常还会增加更多发现），并在与基线相同的条件下控制错误发现率。为证明该原理具有广泛适用性，我们用它改进了大量多重检验程序：（i）在PRDS下，Anchored-BH优于Benjamini-Hochberg（BH）程序，且与Goeman近期提出的closed-BH不可比；（ii）在任意依赖下，Anchored-BY优于Benjamini-Yekutieli（BY）程序，且与closed-BY不可比；（iii）对于双侧高斯p值（在适当协方差条件下），Anchored-2BH优于在两个单侧p值上以一半水平运行两次BH的方法；（iv）Anchored-dBH优于依赖调整的BH；（v）Anchored e-BH优于e-BH，且与closed e-BH不可比；（vi）Anchored SeqStep+改进了原始程序（包括选择性和自适应变体），同时保留有序拒绝结构。所有这些改进均在排序时间或二次时间内完成。附录展示了如何改进Shifted-BH（用于双侧任意相关高斯分布）和NDBH（用于负依赖p值）。
英文摘要
The recent e-closure method can recover every procedure that controls FDR (and other expectation losses). But the recovered e-collection is ``self-referential'' and gives no insight on how to improve the procedure (if improvable), and some recent improvements have been somewhat opaque. We introduce an elementary new technique called anchoring that exploits looseness in existing FDR proofs to enlarge a baseline multiple-testing procedure's self-referential local e-value. The resulting e-closure thus transparently retains every baseline discovery (and usually adding more) and controlling the false discovery rate under the same conditions as the baseline. To show that this principle is broadly applicable, we use it to improve a large suite of multiple testing procedures: (i) Anchored-BH dominates the Benjamini-Hochberg (BH) procedure under PRDS while being incomparable to Goeman's recent closed-BH, (ii) Anchored-BY dominates the Benjamini-Yekutieli (BY) procedure under arbitrary dependence while being incomparable to closed-BY, (iii) For two-sided Gaussian p-values (under appropriate covariance conditions), Anchored-2BH dominates running BH twice at half the level on two one-sided p-values, (iv) Anchored-dBH dominates dependence-adjusted BH, (v) Anchored e-BH dominates e-BH and is incomparable to closed e-BH, (vi) Anchored SeqStep+ improves the original (including selective and adpative variants) while preserving ordered rejection structures. All of these are accomplished in sorting or quadratic time. The appendix shows how to dominate Shifted-BH (for two-sided arbitrarily correlated Gaussians) and NDBH (under negative dependent p-values).
Comments50 pages, 8 figures
