ROBUST INFERENCE VIA MULTIPLIER BOOTSTRAP

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 lea...

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Bibliographic Details
Published in:The Annals of statistics 2020-06, Vol.48 (3), p.1665-1691
Main Authors: Chen, Xi, Zhou, Wen-Xin
Format: Article
Language:English
Subjects:
Bootstrap method
Confidence
Estimating techniques
Hypothesis testing
Least squares method
Probability distribution
Regression analysis
Robustness (mathematics)
Statistical analysis
Statistical inference
Statistical methods
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Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/19-AOS1863