Abstract

Two-sample multiple testing has a wide range of applications. Most of the literature considers simultaneous tests of equality of parameters. The paper takes a different perspective and investigates the null hypotheses that the two support sets are equal. This formulation of the testing problem is motivated by the fact that in many applications where the two parameter vectors being compared are both sparse, one might be more concerned about the detection of differential sparsity structures rather than the difference in parameter magnitudes. Focusing on this type of problem, we develop a general approach, which adapts the newly proposed symmetry data aggregation tool combined with a novel double thresholding (DT) filter. The DT filter first constructs a sequence of pairs of ranking statistics that fulfill global symmetry properties and then chooses two data-driven thresholds along the ranking to simultaneously control the false discovery rate (FDR) and maximize the number of rejections. Several applications of the methodology are given including high-dimensional linear models and Gaussian graphical models. We show that the proposed method is able to asymptotically control the FDR and have power guarantee under certain conditions. Numerical results confirm the effectiveness and robustness of DT in FDR control and detection ability.

摘要

两样本多重检验具有广泛的应用。大多数文献都考虑了参数相等性的同时测试。本文采用不同的视角，研究了两个支持集相等的原假设。提出这种测试问题的动机是，在许多被比较的两个参数向量都是稀疏的应用中，人们可能更关心差分稀疏结构的检测，而不是参数大小的差异。针对此类问题，我们开发了一种通用方法，该方法采用新提出的对称数据聚合工具与新颖的双阈值 (DT) 过滤器相结合。DT 过滤器首先构建一系列满足全局对称属性的排名统计对，然后沿着排名选择两个数据驱动的阈值以同时控制错误发现率 (FDR) 并最大化拒绝次数。给出了该方法的几个应用，包括高维线性模型和高斯图形模型。我们表明，所提出的方法能够渐进控制 FDR，并在特定条件下具有功率保证。数值结果证实了 DT 在 FDR 控制和检测能力方面的有效性和鲁棒性。给出了该方法的几个应用，包括高维线性模型和高斯图形模型。我们表明，所提出的方法能够渐进控制 FDR，并在特定条件下具有功率保证。数值结果证实了 DT 在 FDR 控制和检测能力方面的有效性和鲁棒性。给出了该方法的几个应用，包括高维线性模型和高斯图形模型。我们表明，所提出的方法能够渐进控制 FDR，并在特定条件下具有功率保证。数值结果证实了 DT 在 FDR 控制和检测能力方面的有效性和鲁棒性。