Exceedance Control of the False Discovery Proportion Via High Precision Inversion Method of Berk-Jones Statistics.

Exceedance control of the false discovery proportion (FDP) can provide an interpretable method for addressing the variability in the false discovery proportion estimates. Exceedance control of FDP can be viewed as constructing a confidence interval for FDP and as such inverting a hypothesis test is a viable method for achieving exceedance control. A novel powerful approach for exceedance control is presented based on using a directional Berk-Jones goodness-of-fit statistic. The approach employs a high-precision implementation procedure to accurately compute confidence envelopes for FDP. The procedure is compared against other methods and generalized to include other goodness-of-fit statistics that follow an isotropy condition.