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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 replicability claims. The suggested procedures first select the promising features from each study solely based on that study, and then test for replicability only the features that were selected in both studies. We incorporate the plug-in estimates of the fraction of null hypotheses in one study among the selected hypotheses by the other study. Since the fraction of nulls in one study among the selected features from the other study is typically small, the power gain can be remarkable. We provide theoretical guarantees for the control of the appropriate error rates, as well as simulations that demonstrate the excellent power properties of the suggested procedures. We demonstrate the usefulness of our procedures on real data examples from two application fields: behavioural genetics and microarray studies.
Advancement in technology has generated abundant high-dimensional data that allows integration of multiple relevant studies. Due to their huge computational advantage, variable screening methods based on marginal correlation have become promising alt
A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a true research hypothesis subject to the constraint of type I error. When there is more than one test,
Consider a two-by-two factorial experiment with more than 1 replicate. Suppose that we have uncertain prior information that the two-factor interaction is zero. We describe new simultaneous frequentist confidence intervals for the 4 population cell m
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 configurati
We offer a non-parametric plug-in estimator for an important measure of treatment effect variability and provide minimum conditions under which the estimator is asymptotically efficient. The stratum specific treatment effect function or so-called bli