A Predictive Density Criterion for Selecting Non-Nested Linear Models and Comparison with Other Criteria

Abstract

The mean squared-errors of forecasts (MSEF) is a statistic used to evaluate post-sample prediction performance. The MSEF has been used as a descriptive measure, but its exact distribution can be derived either from a sample theoretical or from a Bayesian perspective if the MSEF is computed from a linear regression model. In this paper, Bayesian and sampling distributions of the MSEF are derived, and it is suggested that the MSEF may be used as a statistic for linear model selection. Using sampling experiments, we compare the MSEF criterion with other model selection criteria. The organization of the paper is as follows. In section 2, we give the Bayesian and sampling distributions of the MSEF. In section 3, after presenting Akaike’s information criterion, AIC, [Akaike (1974)], Efron’s confidence interval for the mean squared errors, the N- and J-tests, we make sampling experiments to compare the Bayesian MSEF criterion with these other criteria.