AISM 52, 57-70

## 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.

**Source**
( TeX , DVI )