Regularization in statistics |
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| Authors: | Peter J Bickel Bo Li Alexandre B Tsybakov Sara A van de Geer Bin Yu Teófilo Valdés Carlos Rivero Jianqing Fan Aad van der Vaart |
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| Affiliation: | (1) Department of Statistics, University of California at Berkeley, USA;(2) School of Economics and Management, Tsinghua University, China;(3) Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI, France;(4) Seminar für Statistik, ETH Zürich, Switzerland;(5) Department of Statistics and Operational Research, Complutense University of Madrid, Spain;(6) Department of Operations Research and Financial Engineering, Princeton University, USA;(7) Department of Mathematics, Vrije Universiteit Amsterdam, Netherlands |
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| Abstract: | 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. |
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| Keywords: | Regularization linear regression nonparametric regression boosting covariance matrix principal component bootstrap subsampling model selection |
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