Balanced control of generalized error rates
本文提出同时控制多个假设检验中k个或更多错误拒绝概率（k-FWER）的方法，包括单步和逐步程序，并考虑错误发现比例（FDP）的控制，通过重抽样和子抽样方法实现渐近平衡。
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 γ and α, P{FDP>γ}≤α, 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.