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RESEARCH PRODUCT

A generalized predictive criterion for model selection

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Given a random sample from some unknown model belonging to a finite class of parametric models, assume that the estimate of the density of a future observation is of interest San Martini & Spezzaferri (1984) proposed for this problem a predictive criterion based on the logarithmic utility function. The present authors investigate a generalization of this criterion that uses as a loss function an element of the class of α-divergences discussed by Ali & Silvey (1966) and Csiszar (1967). They also discuss briefly the case in which the class of models considered is not exhaustive. Un critere de prevision generalise pour la selection de modeles Supposons que l'on cherche a estimer la densite d'une observation future a partir d'un echantillon aleatoire issu d'un modele inconnu appartenant a une classe finie de modeles parametriques. Pour resoudre ce probleme, San Martini & Spezzaferri (1984) ont propose l'emploi d'un critere de prevision base sur la fonction d'utilite logarithmique. Les auteurs du present article etudient une generalisation de ce critere qui s'appuie sur la classe de fonctions de perte appelees α-divergences par Ali & Silvey (1966) et Csiszar (1967). Ils abordent aussi brievement le cas ou la classe de modeles consideren'est pas exhaustive.