Mean Estimation and Regression Under Heavy-Tailed Distributions: A Survey

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data in both the univariate and multivariate settings. We focus on estimators based on median-of-means techniques, but other...

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Bibliographic Details
Published in:Foundations of computational mathematics Vol. 19; no. 5; pp. 1145 - 1190
Main Authors: Lugosi, Gábor, Mendelson, Shahar
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2019
Springer Nature B.V
Subjects:
Applications of Mathematics
Computer Science
Economics
Estimators
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Regression
Statistical analysis
62G05
Statistical learning
Regression function estimation
Robustness
Mean estimation
62G35
Heavy-tailed distributions
62G15
ISSN:1615-3375, 1615-3383
Online Access:Get full text
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Summary:We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data in both the univariate and multivariate settings. We focus on estimators based on median-of-means techniques, but other methods such as the trimmed-mean and Catoni’s estimators are also reviewed. We give detailed proofs for the cornerstone results. We dedicate a section to statistical learning problems—in particular, regression function estimation—in the presence of possibly heavy-tailed data.
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ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-019-09427-x