ROBUST HIGH-DIMENSIONAL TUNING FREE MULTIPLE TESTING

• 成果类型: Article
• 署名作者: Fan, Jianqing; Lou, Zhipeng; Yu, Mengxin
• 署名单位: Princeton University; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; University of Pennsylvania
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2322
• 发表日期: 2023
• 页码: 2093-2115
• 关键词: false discovery rate; rna-seq; bootstrap approximations; quantile regression; efficient approach; 2-sample test; U-statistics; M-ESTIMATORS; REPRESENTATION; asymptotics

摘要

A stylized feature of high-dimensional data is that many variables have heavy tails, and robust statistical inference is critical for valid large-scale statistical inference. Yet, the existing developments such as Winsorization, Huberization and median of means require the bounded second moments and involve variable-dependent tuning parameters, which hamper their fidelity in applications to large-scale problems. To liberate these constraints, this paper revisits the celebrated Hodges-Lehmann (HL) estimator for estimating location parameters in both the one- and two-sample problems, from a nonasymptotic perspective. Our study develops Berry-Esseen inequality and Cramer-type moderate deviation for the HL estimator based on newly developed nonasymptotic Bahadur representation and builds data-driven confidence intervals via a weighted bootstrap approach. These results allow us to extend the HL estimator to large-scale studies and propose tuning-free and moment-free high-dimensional inference procedures for testing global null and for large-scale multiple testing with false discovery proportion control. It is convincingly shown that the resulting tuning-free and moment-free methods control false discovery proportion at a prescribed level. The simulation studies lend further support to our developed theory.