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Competition-based approach to controlling the false discovery rate (FDR)recently rose to prominence when, generalizing it to sequential hypothesistesting, Barber and Cand\`es used it as part of their knockoff-filter. Controlof the FDR implies that the, arguably more important, false discoveryproportion is only controlled in an average sense. We present TDC-SB and TDC-UBthat provide upper prediction bounds on the FDP in the list of discoveriesgenerated when controlling the FDR using competition. Using simulated and realdata we show that, overall, our new procedures offer significantly tighterupper bounds than ones obtained using the recently published approach ofKatsevich and Ramdas, even when the latter is further improved using theinterpolation concept of Goeman et al.

Bounding the FDP in competition-based control of the FDR