In sparse large-scale testing problems where the false discovery proportion (FDP) is highly variable, the false discovery exceedance (FDX) provides a valuable alternative to the widely used false discovery rate (FDR). We develop an empirical Bayes approach to controlling 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 FDX constraint. We propose a data-driven FDX procedure that emulates the oracle via carefully designed computational shortcuts. We investigate the empirical performance of the proposed method using simulations and illustrate the merits of FDX control through an application for identifying abnormal stock trading strategies.
翻译:假发现比例(FDP)变化很大,虚假发现超额(FDX)为广泛使用的虚假发现率(FDR)提供了宝贵的替代方法。我们开发了一种经验型海湾控制FDX的方法。我们证明,对于两组模式的独立假设和高斯模式符合可兑换性条件的依附假设,基于当地虚假发现率(lfdr)的等级和门槛的甲骨文决定规则是最佳的,因为受FDX限制,权力最大化。我们提议了一个数据驱动的FDX程序,通过精心设计的计算快捷方式仿照甲骨。我们用模拟方法调查了拟议方法的经验表现,并通过应用查明异常股票交易战略来说明FDX控制的好处。