We are concerned with testing replicability hypotheses for many endpoints simultaneously. This constitutes a multiple test problem with composite null hypotheses. Traditional -values, which are computed under least favorable parameter configurations (LFCs), are over-conservative in the case of composite null hypotheses. As demonstrated in prior work, this poses severe challenges in the multiple testing context, especially when one goal of the statistical analysis is to estimate the proportion of true null hypotheses. Randomized -values have been proposed to remedy this issue. In the present work, we discuss the application of randomized -values in replicability analysis. In particular, we introduce a general class of statistical models for which valid, randomized -values can be calculated easily. By means of computer simulations, we demonstrate that their usage typically leads to a much more accurate estimation of than the LFC-based approach. Finally, we apply our proposed methodology to a real data example from genomics.

中文翻译：

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多重测试的随机值及其在可复制性分析中的应用

我们关心同时测试许多端点的可复制性假设。这构成了具有复合零假设的多重检验问题。在最不利参数配置 (LFC) 下计算的传统值在复合零假设的情况下过于保守。正如之前的工作所证明的，这在多重测试环境中提出了严峻的挑战，特别是当统计分析的一个目标是估计真零假设的比例时。已经提出了随机化的值来解决这个问题。在目前的工作中，我们讨论了随机值在可复制性分析中的应用。特别是，我们介绍了一类通用的统计模型，其有效的、随机的-值可以很容易地计算出来。通过计算机模拟，我们证明了它们的使用通常会导致比基于 LFC 的方法更准确的估计。最后，我们将我们提出的方法应用于基因组学的真实数据示例。