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

• 成果类型: Article
• 署名作者: Xia, Yin; Cai, T. Tony; Sun, Wenguang
• 署名单位: Fudan University; University of Pennsylvania; University of Southern California
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1611585
• 发表日期: 2020
• 页码: 1236-1250
• 关键词: false discovery rate; environment interactions; null hypotheses; multiple; PROPORTION; networks; tests

摘要

This 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.