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We are concerned with testing replicability hypotheses for many endpoints simultaneously. This constitutes a multiple test problem with composite null hypotheses. Traditional $p$-values, which are computed under least favourable parameter configurations, 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 $pi_0$ of true null hypotheses. Randomized $p$-values have been proposed to remedy this issue. In the present work, we discuss the application of randomized $p$-values in replicability analysis. In particular, we introduce a general class of statistical models for which valid, randomized $p$-values can be calculated easily. By means of computer simulations, we demonstrate that their usage typically leads to a much more accurate estimation of $pi_0$. Finally, we apply our proposed methodology to a real data example from genomics.
Given a family of null hypotheses $H_{1},ldots,H_{s}$, we are interested in the hypothesis $H_{s}^{gamma}$ that at most $gamma-1$ of these null hypotheses are false. Assuming that the corresponding $p$-values are independent, we are investigating com
We are concerned with multiple test problems with composite null hypotheses and the estimation of the proportion $pi_{0}$ of true null hypotheses. The Schweder-Spjo tvoll estimator $hat{pi}_0$ utilizes marginal $p$-values and only works properly if t
Replicability analysis aims to identify the findings that replicated across independent studies that examine the same features. We provide powerful novel replicability analysis procedures for two studies for FWER and for FDR control on the replicabil
When testing for replication of results from a primary study with two-sided hypotheses in a follow-up study, we are usually interested in discovering the features with discoveries in the same direction in the two studies. The direction of testing in
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to controlling an