  When multiple hypotheses are tested, interest is often in ensuring that the
proportion of false discoveries (FDP) is small with high confidence. In this
paper, confidence upper bounds for the FDP are constructed, which are
simultaneous over all rejection cut-offs. In particular this allows the user to
select a set of hypotheses post hoc such that the FDP lies below some constant
with high confidence. Our method uses permutations to account for the
dependence structure in the data. So far only Meinshausen provided an exact,
permutation-based and computationally feasible method for simultaneous FDP
bounds. We provide an exact method, which uniformly improves this procedure.
Further, we provide a generalization of this method. It lets the user select
the shape of the simultaneous confidence bounds. This gives the user more
freedom in determining the power properties of the method. Interestingly,
several existing permutation methods, such as Significance Analysis of
Microarrays (SAM) and Westfall and Young's maxT method, are obtained as special
cases.
