The Simes Method for Multiple Hypothesis Testing With Positively Dependent Test Statistics
证明了当检验统计量存在正相关时，Simes方法仍能控制第一类错误概率，比Bonferroni方法更有效，适用于多重假设检验场景。
Abstract The Simes method for testing intersection of more than two hypotheses is known to control the probability of type I error only when the underlying test statistics are independent. Although this method is more powerful than the classical Bonferroni method, it is not known whether it is conservative when the test statistics are dependent. This article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple-hypothesis testing situations, the Simes method indeed controls the probability of type I error. This extends some results established very recently in the special case of two hypotheses.