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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| Published in | Foundations of computational mathematics Vol. 19; no. 5; pp. 1145 - 1190 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.10.2019
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1615-3375 1615-3383 |
| DOI | 10.1007/s10208-019-09427-x |
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| Abstract | 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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| AbstractList | 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. |
| Audience | Academic |
| Author | Mendelson, Shahar Lugosi, Gábor |
| Author_xml | – sequence: 1 givenname: Gábor surname: Lugosi fullname: Lugosi, Gábor email: gabor.lugosi@upf.edu organization: Department of Economics and Business, Pompeu Fabra University, ICREA, Barcelona Graduate School of Economics – sequence: 2 givenname: Shahar surname: Mendelson fullname: Mendelson, Shahar organization: Mathematical Sciences Institute, The Australian National University, LPSM, Sorbonne University |
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| SubjectTerms | 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 |
| Title | Mean Estimation and Regression Under Heavy-Tailed Distributions: A Survey |
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