摘要：Consider the multiple testing problem of testing m null hypotheses 𝐻1,…,𝐻𝑚, among which 𝑚0 hypotheses are truly null. Given the P-values for each hypothesis, the question of interest is
how to combine the P-values to find out which hypotheses are false nulls and possibly to make
a statistical inference on 𝑚0. Benjamini and Hochberg proposed a classical procedure that can
control the false discovery rate (FDR). The FDR control is a little bit unsatisfactory in that it
only concerns the expectation of the false discovery proportion (FDP). The control of the actual
random variable FDP has recently drawn much attention. For any level 1−𝛼, this paper proposes
a procedure to construct an upper prediction bound (UPB) for the FDP for a fixed rejection
region. When 1−𝛼=50%, our procedure is very close to the classical Benjamini and Hochberg
procedure. Simultaneous UPBs for all rejection regions' FDPs and the upper confidence bound
for the unknown 𝑚0 are presented consequently. This new proposed procedure works for finite
samples and hence avoids the slow convergence problem of the asymptotic theory.
