Abstract
As their name suggests, competition-based procedures use direct head-to-head competition between the originally observed score and a randomly generated null score for each hypothesis in order to control the FDR amongst the resulting list of discoveries. In this thesis we extend this competition framework and develop multiple testing procedures that utilize competition between the original scores and multiple, rather than a single, set of null scores. We construct these methods in the frameworks of peptide identification through target-decoy competition and the classical linear regression problem with Barber and Cand`es' recent knockoff procedure. In both these cases we show through simulations and real data experiments that utilizing multiple competition properly can lead to significant power gains without losing FDR control.
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