TWO-SAMPLE TESTING OF HIGH-DIMENSIONAL LINEAR REGRESSION COEFFICIENTS VIA COMPLEMENTARY SKETCHING

• 成果类型: Article
• 署名作者: Gao, Fengnan; Wang, Tengyao
• 署名单位: Fudan University; University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2216
• 发表日期: 2022
• 页码: 2950-2972
• 关键词: anova

摘要

We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and response vectors along directions that are complementary in sign in a subset of the coordinates, a process which we call complementary sketching. The resulting projected covariates and responses are aggregated to form two test statistics, which are shown to have essentially optimal asymptotic power under a Gaussian design when the difference between the two regression coefficients is sparse and dense respectively. Simulations confirm that our methods perform well in a broad class of settings and an application to a large single-cell RNA sequencing dataset demonstrates its utility in the real world.