**Christopher Genovese and Larry Wasserman**

Multiple testing methods to control the False Discovery Rate (FDR),
the expected proportion of falsely rejected null hypotheses among
all rejections) have received much attention. It
can be valuable instead to control not the mean of this false
discovery proportion (FDP) but the probability that the FDP exceeds
a specified bound. In this paper, we construct a general class of
methods for exceedance control of FDP based on inverting tests of
uniformity. The method also produces a confidence envelope for the
FDP as a function of rejection threshold. We discuss how to
select a procedure with good power.

*Keywords:* Multiple Testing, p-values, False Discovery Rate

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