In many applications, the process of identifying a specific feature of interest often involves testing multiple hypotheses for their joint statistical significance. 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 study, we present a new approach called joint mirror (JM) procedure that effectively detects such features while maintaining false discovery rate (FDR) control in finite samples. The JM procedure employs an iterative method that gradually shrinks the rejection region based on progressively revealed information until a conservative estimate of the false discovery proportion (FDP) is below the target FDR level. Additionally, we introduce a more stringent error measure, known as the modified FDR (mFDR), which assigns weights to each false discovery based on its number of null components. We demonstrate that, under appropriate assumptions, the JM procedure controls the mFDR in finite samples. To implement the JM procedure, we propose an efficient algorithm that can incorporate partial ordering information. Through extensive simulations, we demonstrate that our procedure effectively controls the mFDR and enhances statistical power across various scenarios. Finally, we showcase the utility of our method by applying it to real-world mediation and replicability analyses.

翻译：在许多应用中，识别特定感兴趣特征的过程往往涉及对多个假设进行联合统计显著性检验。例如，中介分析需同时检验暴露-中介效应和中介-结局效应的存在性，而可重复性分析旨在识别在多个独立实验中均具有统计显著性的联合信号。本研究提出一种名为联合镜像程序的新方法，该方法能在有限样本中有效检测此类特征，同时控制错误发现率。联合镜像程序通过迭代方法逐步收缩拒绝域，基于逐步揭示的信息最终使错误发现比例的保守估计值低于目标错误发现率水平。此外，我们引入一种更严格的误差度量——修正错误发现率，该度量根据每个错误发现中零成分的数量对其赋予权重。我们证明，在适当假设下，联合镜像程序能在有限样本中控制修正错误发现率。为实施该程序，我们提出一种可整合偏序信息的高效算法。通过广泛仿真，我们证明该方法能在多种场景下有效控制修正错误发现率并提升统计功效。最后，通过将其应用于实际中介分析与可重复性分析，我们展示了该方法的实用性。