A generalized predictive criterion for model selection

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 alpha-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.