Regularization in statistics

This paper is a selective review of the regularization methods scattered in statistics literature. We introduce a general conceptual approach to regularization and fit most existing methods into it. We have tried to focus on the importance of regularization when dealing with today's high-dimens...

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Bibliographic Details
Published inTest (Madrid, Spain) Vol. 15; no. 2; pp. 271 - 344
Main Authors Bickel, Peter J., Li, Bo, Tsybakov, Alexandre B., van de Geer, Sara A., Yu, Bin, Valdés, Teófilo, Rivero, Carlos, Fan, Jianqing, van der Vaart, Aad
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.09.2006
Sociedad Española de Estadística e Investigación Operativa
Subjects
Regularization - linear regression - nonparametric regression - boosting - covariance matrix - principal component - bootstrap - subsampling - model selection
Regularization methods
Statistics
Studies
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Summary:This paper is a selective review of the regularization methods scattered in statistics literature. We introduce a general conceptual approach to regularization and fit most existing methods into it. We have tried to focus on the importance of regularization when dealing with today's high-dimensional objects: data and models. A wide range of examples are discussed, including nonparametric regression, boosting, covariance matrix estimation, principal component estimation, subsampling.[PUBLICATION ABSTRACT]
ISSN:1133-0686
1863-8260
DOI:10.1007/BF02607055