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 inFoundations of computational mathematics Vol. 19; no. 5; pp. 1145 - 1190
Main Authors Lugosi, Gábor, Mendelson, Shahar
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2019
Springer
Springer Nature B.V
Subjects
Applications of Mathematics
Average
Computer Science
Economics
Estimation theory
Estimators
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematical research
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Regression
Regression analysis
Statistical analysis
Spain
62G05
Statistical learning
Regression function estimation
Robustness
Mean estimation
62G35
Heavy-tailed distributions
62G15
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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.
Bibliography:ObjectType-Article-1
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ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-019-09427-x