Simultaneous control of all false discovery proportions in large-scale multiple hypothesis testing
研究了基于Simes局部检验的封闭检验程序，提出一种快速精确的捷径算法，证明在信号足够时该方法能有效控制错误发现比例，且置信界是真实错误发现比例的一致估计。
Summary Closed testing procedures are classically used for familywise error rate control, but they can also be used to obtain simultaneous confidence bounds for the false discovery proportion in all subsets of the hypotheses, allowing for inference robust to post hoc selection of subsets. In this paper we investigate the special case of closed testing with Simes local tests. We construct a novel fast and exact shortcut and use it to investigate the power of this approach when the number of hypotheses goes to infinity. We show that if a minimal level of signal is present, the average power to detect false hypotheses at any desired false discovery proportion does not vanish. Additionally, we show that the confidence bounds for false discovery proportion are consistent estimators for the true false discovery proportion for every nonvanishing subset. We also show close connections between Simes-based closed testing and the procedure of Benjamini and Hochberg.