Two general classes of multiple decision functions, where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery rate (FDR), are described. These classes offer the possibility that optimal multiple decision functions with respect to a pre-specified Type II error criterion, such as the missed discovery rate (MDR), could be found which control the FWER or FDR Type I error rates. The gain in MDR of the associated FDR-controlling procedure relative to the well-known Benjamini–Hochberg procedure is demonstrated via a modest simulation study with gamma-distributed component data. Such multiple decision functions may have the potential of being utilized in multiple testing, specifically in the analysis of high-dimensional data sets.

中文翻译：

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强控制 FWER 和 FDR 的多决策函数类

描述了多决策函数的两个一般类别，其中第一类的每个成员强烈控制家庭错误率 (FWER)，而第二类的每个成员强烈控制错误发现率 (FDR)。这些类别提供了一种可能性，即可以找到与预先指定的 II 类错误标准（例如遗漏发现率 (MDR)）相关的最佳多重决策函数，这些函数控制 FWER 或 FDR I 类错误率。相关的 FDR 控制程序相对于著名的 Benjamini-Hochberg 程序的 MDR 增益通过使用伽马分布分量数据的适度模拟研究来证明。这种多重决策函数有可能被用于多重测试，特别是在高维数据集的分析中。