多重测试中的下界：一个基于去随机化代理的框架
Lower bounds in multiple testing: A framework based on derandomized proxies
摘要：
在多重测试中，大部分工作都集中在指定控制错误发现率（FDR）的程序上，而相对较少关注被称为错误未发现率（FNR）的相应II型错误。最近的一系列多测试工作已经开始研究FDR和FNR之间的权衡，并提供依赖于模型结构的程序性能的下界。然而，到目前为止，缺乏一个通用的方法来获得广泛的一类模型的下界。本文介绍了一种基于去随机化的分析策略，并通过对各种具体模型的应用加以说明。我们的主要结果是元定理，给出了一个通用的配方获得的组合FDR和FNR的下界。我们通过推导几个模型的明确界限来说明这个元定理，包括依赖性，尺度变换的替代品和非高斯分布的实例。我们提供了一些这些下界的数值模拟，并显示出密切关系的Benjamini-Hochberg（BH）算法的实际性能。
英文摘要：
The large bulk of work in multiple testing has focused on specifying procedures that control the false discovery rate (FDR), with relatively less attention being paid to the corresponding Type II error known as the false non-discovery rate (FNR). A line of more recent work in multiple testing has begun to investigate the tradeoffs between the FDR and FNR and to provide lower bounds on the performance of procedures that depend on the model structure. Lacking thus far, however, has been a general approach to obtaining lower bounds for a broad class of models. This paper introduces an analysis strategy based on derandomization, illustrated by applications to various concrete models. Our main result is meta-theorem that gives a general recipe for obtaining lower bounds on the combination of FDR and FNR. We illustrate this meta-theorem by deriving explicit bounds for several models, including instances with dependence, scale-transformed alternatives, and non-Gaussian-like distributions. We provide numerical simulations of some of these lower bounds, and show a close relation to the actual performance of the Benjamini-Hochberg (BH) algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
