A NOTE ON THE UNIFICATION OF THE AKAIKE INFORMATION CRITERION

To measure the distance between a robust function evaluated under the true regression model and under a fitted model, we propose generalized Kullback-Leibler information. Using this generalization we have devel oped three robust model selection criteria, AICR, AICCR* and AICCR, t hat allow the selection of candidate models that not only fit the majo rity of the data but also take into account non-normally distributed e rrors. The AICR and AICCR criteria can unify most existing Akaike inf ormation criteria; three examples of such unification are given. Simul ation studies are presented to illustrate the relative performance of each criterion.