GAP: A General Framework for Information Pooling in Two-Sample Sparse Inference

原文摘要

Yin Xiaa, T. Tony Caib & Wenguang Sunc*a Department of Statistics, School of Management, Fudan University, Shanghai, China; b Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA; c Department of Data Sciences and Operations, University of Southern California, Los Angeles, CAColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.CONTACT Wenguang Sun wenguans@marshall.usc.edu Department of Data Sciences and Operations, University of Southern California.AbstractThis article develops a general framework for exploiting the sparsity information in two-sample multiple testing problems. We propose to first construct a covariate sequence, in addition to the usual primary test statistics, to capture the sparsity structure, and then incorporate the auxiliary covariates in inference via a three-step algorithm consisting of grouping, adjusting and pooling (GAP). The GAP procedure provides a simple and effective framework for information pooling. An important advantage of GAP is its capability of handling various dependence structures such as those arise from high-dimensional linear regression, differential correlation analysis, and differential network analysis. We establish general conditions under which GAP is asymptotically valid for false discovery rate control, and show that these conditions are fulfilled in a range of settings, including testing multivariate normal means, high-dimensional linear regression, differential covariance or correlation matrices, and Gaussian graphical models. Numerical results demonstrate that existing methods can be significantly improved by the proposed framework. The GAP procedure is illustrated using a breast cancer study for identifying gene–gene interactions.

摘要来源：OpenAlex