Flexible control of the median of the false discovery proportion
提出一种仅需p值向量即可灵活控制错误发现比例中位数的多重检验方法，允许在查看数据后自由选择显著性水平，且不假设独立性，计算复杂度与假设数量成线性关系。
Summary We introduce a multiple testing procedure that controls the median of the proportion of false discoveries in a flexible way. The procedure requires only a vector of p-values as input and is comparable to the Benjamini–Hochberg method, which controls the mean of the proportion of false discoveries. Our method allows free choice of one or several values of $ \alpha $ after seeing the data, unlike the Benjamini–Hochberg procedure, which can be very anti-conservative when $ \alpha $ is chosen post hoc. We prove these claims and illustrate them with simulations. The proposed procedure is inspired by a popular estimator of the total number of true hypotheses. We adapt this estimator to provide simultaneously median unbiased estimators of the proportion of false discoveries, valid for finite samples. This simultaneity allows for the claimed flexibility. Our approach does not assume independence. The time complexity of our method is linear in the number of hypotheses, after sorting the p-values.