Large-Scale Two-Sample Comparison of Support Sets

作     者：Geng, Haoyu Cui, Xiaolong Ren, Haojie Zou, Changliang 

作者机构：Nankai Univ Sch Stat & Data Sci LPMC KLMDASR Tianjin Peoples R China Nankai Univ LEBPS Tianjin Peoples R China Shanghai Jiao Tong Univ Sch Math Sci Shanghai Peoples R China 

出 版 物：《JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION》 (美国统计学会志)

年 卷 期：2024年第119卷第546期

页      面：1604-1618页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 

基　　金：China National Key Ramp D Program [2019YFC1908502, 2022YFA1003703, 2022YFA1003802, 2022YFA1003803] NNSF of China grants [11925106, 12231011, 11931001, 11971247, 1210010142] Shanghai Sailing Program 

主　　题：Data-driven methods Gaussian graphical models High-dimensional models Multiple testing Sample-splitting Uniform convergence 

摘      要：Two-sample multiple testing has a wide range of applications. Most of the literature considers simultaneous tests of equality of parameters. The article 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. for this article are available online.