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 problems, 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 under certain conditions. Numerical results confirm the effectiveness and robustness of DT in FDR control and detection ability in many settings.
Haojie Ren is currently an Associate Professor in School of Mathematical Sciences, Shanghai Jiao Tong University. Prior to this, she was an Eberly Postdoc Fellow in the Department of Statistics, The Pennsylvania State University, under the supervision of Professor Runze Li from 2019 to 2021. She received her B.S, M.S, and Ph.D. in Statistics from Nankai University in 2013, 2016, 2018, respectively. Her PhD supervisor is Professor Changliang Zou. Haojie's research interests include massive data analysis, on-line monitoring and diagnosis, high-dimensional inference, change-point detection and outlier identification.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai