BALANCED CONTROL OF GENERALIZED ERROR RATES

• 成果类型: Article
• 署名作者: Romano, Joseph P.; Wolf, Michael
• 署名单位: Stanford University; Stanford University; University of Zurich
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS734
• 发表日期: 2010
• 页码: 598-633
• 关键词: false discovery rate; MULTIPLE TEST PROCEDURES; bootstrap

摘要

Consider the problem of testing s hypotheses simultaneously. In this paper, we derive methods which control the generalized family-wise error rate given by the probability of k or more false rejections, abbreviated k-FWER. We derive both single-step and step-down procedures that control the k-FWER in finite samples or asymptotically, depending on the situation. Moreover, the procedures are asymptotically balanced in an appropriate sense. We briefly consider control of the average number of false rejections. Additionally, we consider the false discovery proportion (FDP), defined as the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). Here, the goal is to construct methods which satisfy, for given gamma and alpha, P{FDP > gamma} <= alpha, at least asymptotically. Special attention is paid to the construction of methods which implicitly take into account the dependence structure of the individual test statistics in order to further increase the ability to detect false null hypotheses. A general resampling and subsampling approach is presented which achieves these objectives, at least asymptotically.