Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

A generalized Cp criterion for Gaussian model selection


Code(s) de Classification MSC:

Résumé: This paper is mainly devoted to a precise analysis of what kind of penalties should be used in order to perform model selection via the minimization of a penalized least-squares type criterion within some general Gaussian framework. As compared to our previous paper on this topic (Birg\'e and Massart, 2001), more elaborate forms of the penalties are given which are shown to be, in some sense, optimal. We also provide risk bounds with explicit absolute constants and an asymptotic evaluation of the risk which generalizes the one of Shibata (1981) to our new penalties. Some applications to the estimation of change points for a signal in Gaussian noise are also developed. We finally present a practical strategy, based on sharp lower bounds for the penalty function, to design the penalty from the data when the amount of noise is unknown.

Mots Clés: Gaussian linear regression ; variable selection ; model selection ; Mallows' $C_p$ ; penalized least-squares

Date: 2001-04-02

Prépublication numéro: PMA-647