  In large-scale multiple hypothesis testing problems, the false discovery
exceedance (FDX) provides a desirable alternative to the widely used false
discovery rate (FDR) when the false discovery proportion (FDP) is highly
variable. We develop an empirical Bayes approach to control the FDX. We show
that, for independent hypotheses from a two-group model and dependent
hypotheses from a Gaussian model fulfilling the exchangeability condition, an
oracle decision rule based on ranking and thresholding the local false
discovery rate (lfdr) is optimal in the sense that the power is maximized
subject to the FDX constraint. We propose a data-driven FDX procedure that uses
carefully designed computational shortcuts to emulate the oracle rule. We
investigate the empirical performance of the proposed method using both
simulated and real data and study the merits of FDX control through an
application for identifying abnormal stock trading strategies.
