  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.
