In many applications, identifying a single feature of interest requires testing the statistical significance of several hypotheses. Examples include mediation analysis which simultaneously examines the existence of the exposure-mediator and the mediator-outcome effects, and replicability analysis aiming to identify simultaneous signals that exhibit statistical significance across multiple independent experiments. In this work, we develop a novel procedure, named joint mirror (JM), to detect such features while controlling the false discovery rate (FDR) in finite samples. The JM procedure iteratively shrinks the rejection region based on partially revealed information until a conservative false discovery proportion (FDP) estimate is below the target FDR level. We propose an efficient algorithm to implement the method. Extensive simulations demonstrate that our procedure can control the modified FDR, a more stringent error measure than the conventional FDR, and provide power improvement in several settings. Our method is further illustrated through real-world applications in mediation and replicability analyses.

翻译：在许多应用中，识别单个感兴趣的特征需要检验多个假设的统计显著性。例如，中介分析需同时检验暴露-中介变量与中介变量-结果效应的存在性，而可重复性分析则旨在识别在多个独立实验中均具有统计显著性的同步信号。本文提出了一种名为联合镜像（JM）的新程序，用于在有限样本中检测此类特征，同时控制错误发现率（FDR）。该程序基于部分揭示的信息迭代收缩拒绝域，直至保守的错误发现比例（FDP）估计值低于目标FDR水平。我们提出了一种高效算法来实现该方法。大量模拟实验表明，该程序能控制修正后的FDR（一种比传统FDR更严格的误差度量），并在多种场景下提升统计功效。我们进一步通过中介分析与可重复性分析的实际应用验证了该方法。