Gaussian model selection

Birgé, Lucien, and Massart, Pascal. "Gaussian model selection." Journal of the European Mathematical Society 003.3 (2001): 203-268. <http://eudml.org/doc/277724>.

@article{Birgé2001,
abstract = {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.},
author = {Birgé, Lucien, Massart, Pascal},
journal = {Journal of the European Mathematical Society},
keywords = {nonasymptotic point of view; white noise framework; curve estimation; parametric; nonparametric; penalized projection estimators; Bayesian view; nonasymptotic point of view; white noise framework; curve estimation; parametric; nonparametric; penalized projection estimators; Bayesian view},
language = {eng},
number = {3},
pages = {203-268},
publisher = {European Mathematical Society Publishing House},
title = {Gaussian model selection},
url = {http://eudml.org/doc/277724},
volume = {003},
year = {2001},
}

TY - JOUR
AU - Birgé, Lucien
AU - Massart, Pascal
TI - Gaussian model selection
JO - Journal of the European Mathematical Society
PY - 2001
PB - European Mathematical Society Publishing House
VL - 003
IS - 3
SP - 203
EP - 268
AB - 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.
LA - eng
KW - nonasymptotic point of view; white noise framework; curve estimation; parametric; nonparametric; penalized projection estimators; Bayesian view; nonasymptotic point of view; white noise framework; curve estimation; parametric; nonparametric; penalized projection estimators; Bayesian view
UR - http://eudml.org/doc/277724
ER -