False discovery and false nondiscovery rates in single-step multiple testing procedures
False discovery and false nondiscovery rates in single-step multiple testing procedures
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DOI：
10.1214/009053605000000778
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发表时间：
2006-02-01
影响因子：
4.5
通讯作者：
Sarkar, Sanat K.
中科院分区：
文献类型：
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作者：
Sarkar, Sanat K.
错误发现率（FDR）和错误的非发现率（FNR）的结果开发的单步多测试程序。除了验证理想的属性的FDR和FNR的错误率的措施，这些结果扩展了以前已知的结果，提供进一步的见解，特别是在依赖，到FDR和FNR和相关措施的概念。首先，考虑到真和假零假设的固定配置，得到的不等式来解释如何FDR或FNR控制的单步程序，如Bonferroni或Sidak程序，可以潜在地改善。两个家庭的程序，然后构建，一个修改的FDR控制和其他修改的FNR控制Sidak程序。这些被证明控制FDR或FNR下的独立性不太保守，比相应的家庭修改FDR或FNR控制Bonferroni程序。改进的Sidak FDR程序的性能超过其竞争对手的数值研究结果。其次，考虑到混合模型，不同的配置的真和假的零假设被假定为具有一定的概率，结果也来自延伸的一些层的工作的依赖情况。
Results on the false discovery rate (FDR) and the false nondiscovery rate (FNR) are developed for single-step multiple testing procedures. In addition to verifying desirable properties of FDR and FNR as measures of error rates, these results extend previously known results, providing further insights, particularly under dependence, into the notions of FDR and FNR and related measures. First, considering fixed configurations of true and false null hypotheses, inequalities are obtained to explain how an FDR- or FNR-controlling single-step procedure, such as a Bonferroni or Sidak procedure, can potentially be improved. Two families of procedures are then constructed, one that modifies the FDR-controlling and the other that modifies the FNR-controlling Sidak procedure. These are proved to control FDR or FNR under independence less conservatively than the corresponding families that modify the FDR- or FNR-controlling Bonferroni procedure. Results of numerical investigations of the performance of the modified Sidak FDR procedure over its competitors are presented. Second, considering a mixture model where different configurations of true and false null hypotheses are assumed to have certain probabilities, results are also derived that extend some of Storey's work to the dependence case.