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重访两样本 Kolmogorov–Smirnov 型检验：局部显著性水平视角AI 解读

From a multiple testing viewpoint, Kolmogorov–Smirnov (KS)-type tests are union-intersection tests which can be redefined in terms of local levels. The local level perspective offers a new viewpoint on ranges of sensitivity of KS-type tests and the design of new tests. We study the finite and asymptotic local level behavior of weighted KS tests which are either tail, intermediate or central sensitive. Furthermore, we provide new tests with approximately equal local levels…

利用真实零假设比例的插件估计控制族错误率AI 解读

Summary Estimation of the number or proportion of true null hypotheses in multiple-testing problems has become an interesting area of research. The first important work in this field was performed by Schweder and Spjøtvoll. Among others, they proposed to use plug-in estimates for the proportion of true null hypotheses in multiple-test procedures to improve the power. We investigate the problem of controlling the familywise error rate FWER when such estimators are used as…

错误发现率与渐近最优拒绝曲线AI 解读

In this paper we introduce and investigate a new rejection curve for asymptotic control of the false discovery rate (FDR) in multiple hypotheses testing problems. We first give a heuristic motivation for this new curve and propose some procedures related to it. Then we introduce a set of possible assumptions and give a unifying short proof of FDR control for procedures based on Simes’ critical values, whereby certain types of dependency are allowed. This methodology of proof…

依赖性与错误发现率：渐近分析AI 解读

Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing $n$ hypotheses when test statistics are dependent. In this paper we investigate the expected error rate (EER) and the false discovery rate (FDR) in some extreme parameter configurations when $n$ tends to infinity for test statistics being exchangeable under null hypotheses. All results are derived in terms of…