Open Access
June 2020 Robust inference via multiplier bootstrap
Xi Chen, Wen-Xin Zhou
Ann. Statist. 48(3): 1665-1691 (June 2020). DOI: 10.1214/19-AOS1863


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.


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Xi Chen. Wen-Xin Zhou. "Robust inference via multiplier bootstrap." Ann. Statist. 48 (3) 1665 - 1691, June 2020.


Received: 1 March 2018; Revised: 1 May 2019; Published: June 2020
First available in Project Euclid: 17 July 2020

zbMATH: 07241607
MathSciNet: MR4124339
Digital Object Identifier: 10.1214/19-AOS1863

Primary: 62F35 , 62F40
Secondary: 62J05 , 62J15

Keywords: confidence set , heavy-tailed data , multiple testing , multiplier bootstrap , robust regression , Wilks’ theorem

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 3 • June 2020
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