  Competition-based approach to controlling the false discovery rate (FDR)
recently rose to prominence when, generalizing it to sequential hypothesis
testing, Barber and Cand\`es used it as part of their knockoff-filter. Control
of the FDR implies that the, arguably more important, false discovery
proportion is only controlled in an average sense. We present TDC-SB and TDC-UB
that provide upper prediction bounds on the FDP in the list of discoveries
generated when controlling the FDR using competition. Using simulated and real
data we show that, overall, our new procedures offer significantly tighter
upper bounds than ones obtained using the recently published approach of
Katsevich and Ramdas, even when the latter is further improved using the
interpolation concept of Goeman et al.
