Model Selection Using the Estimative and the Approximate p* Predictive Densities

Model selection procedures, based on a simple cross-validation technique and on suitable predictive densities, are taken into account. In particular, the selection criterion involving the estimative predictive density is recalled and a procedure based on the approximate p* predictive density is defined. This new model selection procedure, compared with some other well-known techniques on the basis of the squared prediction error, gives satisfactory results. Moreover, higher-order asymptotic expansions for the selection statistics based on the estimative and the approximate p* predictive densities are derived, whenever a natural exponential model is assumed. These approximations correspond to meaningful modifications of the Akaike's model selection statistic.