发表机构
University of Waterloo（滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究基于E值的程序控制错误发现率的可容许性与完备类，考虑同时和逐点程序，引入支配概念，证明加权平均$\overline{\mathrm{eBH}}$程序构成完备类，得出相关可容许性结果及常数项选择指导，突出其在多重检验中的核心作用。
AI 中文摘要
错误发现率（FDR）是现代多重检验中使用最广泛的误差度量。我们首次全面分析了基于E值的程序在控制FDR方面的可容许性。考虑了同时进行和逐点的程序，并引入了强支配和弱支配的概念。表明每个同时进行的程序都被一个可容许的加权平均闭e - Benjamini - Hochberg（$\overline{\mathrm{eBH}}$）程序强支配，进而弱支配，所以加权平均$\overline{\mathrm{eBH}}$程序构成一个完备类。还得出了关于具有非零常数项的对称$\overline{\mathrm{eBH}}$程序可容许性的结果，并给出了常数项选择的指导。逐点e检验程序在可容许性方面有平行理论，逐点加权平均$\overline{\mathrm{eBH}}$程序构成完备类。这些结果突出了加权平均$\overline{\mathrm{eBH}}$程序在多重检验中的核心作用。
英文摘要
The false discovery rate (FDR) is the most widely used error metric in modern multiple testing. We provide a comprehensive analysis of the admissibility of e-value-based procedures with FDR control. We consider both simultaneous and point procedures and introduce strong and weak notions of dominance. Every simultaneous procedure is strongly, and hence weakly, dominated by an admissible weighted-mean closed e-Benjamini--Hochberg ($\overline{\mathrm{eBH}}$) procedure, and thus weighted-mean $\overline{\mathrm{eBH}}$ procedures form a complete class. Every constant-free weighted-mean $\overline{\mathrm{eBH}}$ procedure is admissible at every level, and we propose two ways for choosing constant-free weights based on side information, such as pre-screening data. Within the symmetric class, the usual mean $\overline{\mathrm{eBH}}$ procedure is the largest element if and only if the FDR level is small enough; otherwise this class has no largest element. We also obtain results on the admissibility of symmetric weighted-mean $\overline{\mathrm{eBH}}$ procedures with non-zero constant terms. Point e-testing procedures have a parallel theory of admissibility. These results highlight the central role of weighted-mean $\overline{\mathrm{eBH}}$ procedures in multiple testing.
Comments55 pages; includes supplementary material; MSC class updated; manuscript otherwise unchanged
