MODEL SELECTION USING THE ESTIMATIVE AND THE APPROXIMATE p^{∗} PREDICTIVE DENSITIES^{†}

PAOLO VIDONI

Department of Statistics, University of Udine, via Treppo 18, I-33100 Udine, Italy

(Received December 16, 1996; revised August 20, 1998)

Abstract. 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.

Key words and phrases: Akaike’s criterion, cross-validation procedure, misspecification statistic, natural exponential model, predictive sample reuse method, squared prediction error.