In this article, we introduce a novel procedure for improving power of multiple testing procedures (MTPs) of interval hypotheses. When testing interval hypotheses the null hypothesis $P$-values tend to be stochastically larger than standard uniform if the true parameter is in the interior of the null hypothesis. The new procedure starts with a set of $P$-values and discards those with values above a certain pre-selected threshold, while the rest are corrected (scaled-up) by the value of the threshold. Subsequently, a chosen family-wise error rate (FWER) or false discovery rate MTP is applied to the set of corrected $P$-values only. We prove the general validity of this procedure under independence of $P$-values, and for the special case of the Bonferroni method, we formulate several sufficient conditions for the control of the FWER. It is demonstrated that this "filtering" of $P$-values can yield considerable gains of power.

中文翻译：

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通过条件化在区间假设的多重测试中获得能力。

在本文中，我们介绍了一种新颖的过程，用于提高区间假设的多重测试过程（MTP）的功能。当检验间隔假设时，如果真实参数在虚假假设的内部，则虚假假设$ P $值往往会随机大于标准均匀值。新过程从一组$ P $值开始，并丢弃那些值超过某个预先选择的阈值的值，而其余值则通过该阈值进行校正（按比例放大）。随后，仅将选择的家庭错误率（FWER）或错误发现率MTP应用于校正后的$ P $值集。我们证明了该程序在$ P $值独立性下的一般有效性，对于Bonferroni方法的特殊情况，我们为控制FWER制定了几个充分条件。