On the underfitting and overfitting sets of models chosen by order selection criteria

Xavier Guyon (1, 2) , Jian-Feng Yao (3)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 MATISSE - UMR 8595 - Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques
3 IRMAR - Institut de Recherche Mathématique de Rennes

We give analytic and non-asymptotic description of both over and underfitting sets for a general class of order selection model. Upper bounds for associated misfitting probabilities are given for various family of models . Consistency of model selection can be derived.

Mots clés: model selection; AIC; BIC; underfitting; overfitting; consistency; regression; auro-regression; Markov random field; stable law

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Xavier Guyon, Jian-Feng Yao. On the underfitting and overfitting sets of models chosen by order selection criteria. Journal of Multivariate Analysis, 1999, 70 (2), pp.221-249. ⟨10.1006/jmva.1999.1828⟩. ⟨hal-00272372⟩