ROBUST INFERENCE VIA MULTIPLIER BOOTSTRAP

• 成果类型: Article
• 署名作者: Chen, Xi; Zhou, Wen-Xin
• 署名单位: New York University; University of California System; University of California San Diego
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1863
• 发表日期: 2020
• 页码: 1665-1691
• 关键词: sub-gaussian estimators; False Discovery Rate; students-t; performance; tests; sums

摘要

This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With heavy-tailed observation noise, finite sample properties of the least squares-based methods, typified by the sample mean, are suboptimal both theoretically and empirically. In this paper, we demonstrate that the adaptive Huber regression, integrated with the multiplier bootstrap procedure, provides a useful robust alternative to the method of least squares. Our theoretical and empirical results reveal the effectiveness of the proposed method, and highlight the importance of having inference methods that are robust to heavy tailedness.