Improved predictive model selection

Abstract

This paper introduces a new information criterion for model selection, based on a predictive distribution which improves the estimative one. The selection statistic is defined as a first-order estimator for the expected Kullback–Leibler information between the true model and the fitted one, obtained by means of the improved predictive procedure. The criterion turns out to be a simple, non-computationally demanding, alternative to the Takeuchi information criterion. Whenever the information identity holds, the Akaike information criterion is recovered as a particular case. The results are obtained in the case of independent, but not necessarily identically distributed, observations. Some applications, related to exponential families of distributions and regression models, are presented.