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**A Generalized Predictive Criterion for Model Selection**

**Mario Trottini and Fulvio Spezzaferri**

### Abstract:

Given a sample of *n* i.i.d. observations generated from some unknown
distribution F, assume that F belongs to one of two parametric models
*M*_{1}, *M*_{2}, and that the estimation of the density of a future
observation is of interest. San Martini and Spezzaferri (1984)
proposed for this problem a predictive criterion based on the Kullback
Leibler divergence between the estimate and the density of the future
observation. In this paper a generalization of this criterion is
presented both using a general class of divergences and relaxing the
assumption that the true model belongs to *M*_{1} or *M*_{2}.

*Keywords:* Model Selection, Gaussian Process, Loss Function, -divergences.

*Heidi Sestrich*

*10/1/1999*
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