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划分原理：多重决策理论中的有力工具AI 解读

A first general principle and nowadays state of the art for the construction of powerful multiple test procedures controlling a multiple level $\alpha$ is the so-called closure principle. In this article we introduce another powerful tool for the construction of multiple decision procedures, especially for the construction of multiple test procedures and selection procedures. This tool is based on a partition of the parameter space and will be called partitioning principle…

多重假设检验与第一类错误的期望次数AI 解读

The performance of multiple test procedures with respect to error control is an old issue. Assuming that all hypotheses are true we investigate the behavior of the expected number of type I errors (ENE) as a characteristic of certain multiple tests controlling the familywise error rate (FWER) or the false discovery rate (FDR) at a prespecified level. We derive explicit formulas for the distribution of the number of false rejections as well as for the ENE for single-step,…

逐步多重检验程序与方向性错误控制AI 解读

One of the most difficult problems occurring with stepwise multiple test procedures for a set of two-sided hypotheses is the control of direc-tional errors if rejection of a hypothesis is accomplished with a directional decision. In this paper we generalize a result for so-called step-down procedures derived by Shaffer to a large class of stepwise or closed multiple test procedures. In a unifying way we obtain results for a large class of order statistics procedures…

可交换检验统计量下逐步下降与逐步上升多重检验的渐近比较AI 解读

In this paper interest is focused on some theoretical investigations concerning the comparison of two popular multiple test procedures, so-called step-down and step-up procedures, in terms of their defining critical values. Such procedures can be applied, for example, to multiple comparisons with a control. In the definition of the critical values for these procedures order statistics play a central role. For $k \epsilon N_0$ fixed we consider the joint cumulative…

双侧检验与单侧置信界AI 解读

Based on the duality between tests and confidence sets we introduce a new method to derive one-sided confidence bounds following the rejection of a null hypothesis with two-sided alternatives. This method imputes that the experimenter is only interested in confidence bounds if the null hypothesis is rejected. Furthermore, we suppose that he is only interested in the direction and a lower confidence bound concerning the distance of the true parameter value to the parameter…