Multiple competition based FDR control
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Competition based FDR control has been commonly used for over a decade in the computational mass spectrometry community [7]. The approach has gained significant popularity in other fields after Barber and Candés recently laid its theoretical foundation in a more general setting that, importantly, included the feature selection problem [1]. Here we consider competition based FDR control where we can generate multiple, rather than a single, competing null score. We offer several methods that can take advantage of these multiple null scores, all of which are based on a novel procedure that rigorously controls the FDR in the finite sample setting, provided its two tuning parameters are set without looking at the data. Because none of our methods clearly dominates all the others in terms of power we also develop a data driven approach, which is based on a novel resampling procedure and which tries to select the most appropriate procedure for the problem at hand. Using extensive simulations, as well as real data, we show that all our procedures seem to largely control the FDR and that our data driven approach offers an arguably overall optimal choice. Moreover, we show using real data that in the peptide detection problem our novel approach can increase the number of discovered peptides by up to 50
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