Gaussian model selection
type: Item
instance of: scholarly article
title: Gaussian model selection
zbMATH Open document ID: 1037.62001
author: L. Birgé
author: Pascal Massart
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2001-01-01T00:00:00Z
review text: Summary: Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models, to nonparametric estimation, for which it provides a very powerful tool that allows adaptation under quite general circumstances. Our approach to model selection also provides a natural connection between the parametric and nonparametric points of view and copes naturally with the fact that a model is not necessarily true. The method is based on the penalization of a least squares criterion which can be viewed as a generalization of Mallows' \(C_p\). A large part of our efforts will be put on choosing properly the list of models and the penalty function for various estimation problems, like classical variable selection or adaptive estimation for various types of \(l_p\)-bodies.
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62C20
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 1656346
zbMATH Keywords: nonasymptotic point of view
zbMATH Keywords: white noise framework
zbMATH Keywords: curve estimation
zbMATH Keywords: parametric
zbMATH Keywords: nonparametric
zbMATH Keywords: penalized projection estimators
zbMATH Keywords: Bayesian view
MaRDI profile type: Publication
full work available at URL: s100970100031
OpenAlex ID: W1995771589
Wikidata QID: Q92198678
DOI: 10.1007/S100970100031
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description: scientific article; zbMATH DE number 1656346