论文标题
多次测试中的下限：基于降低代理的框架
Lower bounds in multiple testing: A framework based on derandomized proxies
论文作者
论文摘要
多次测试中的大量工作集中在指定控制错误发现率（FDR）的过程上，而对相应的II型误差（称为错误的非发现率（FNR））的注意力相对较少。多次测试中最新的工作已经开始研究FDR和FNR之间的权衡，并就取决于模型结构的程序的性能提供了下限。然而，到目前为止，缺乏是为广泛模型获得下限的一般方法。本文介绍了基于降低的分析策略，该策略由应用于各种具体模型的应用说明。我们的主要结果是元理论，它提供了一种一般配方，用于在FDR和FNR的组合中获得下限。我们通过为多种模型得出明确的界限来说明这种元理论，包括具有依赖性的实例，规模转换的替代方案和非高斯样分布。我们提供了其中一些下限的数值模拟，并与Benjamini-Hochberg（BH）算法的实际性能有着密切的关系。
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.
