Criteria for Linear Model

Model selection criteria frequently arise from constructing estimators of discrepancy measures used to assess the disparity between thètrue' model and a tted approximating model. The Akaike (1973) information criterion and its variants result from utilizing Kullback's (1968) directed divergence as the targeted discrepancy. The directed divergence is an asym-metric measure of separation between two statistical models, meaning that an alternate directed divergence may be obtained by reversing the roles of the two models in the deeni-tion of the measure. The sum of the two directed divergences is Kullback's (1968) symmetric divergence. In the framework of linear models, a comparison of the two directed divergences indicates an important distinction between the measures. When used to evaluate tted approximating models which are improperly speciied, the directed divergence which serves as the basis for AIC is more sensitive towards detecting overrtted models, whereas its counterpart is more sensitive towards detecting underrtted models. Since the symmetric divergence combines the information in both measures, it functions as a gauge of model disparity which is arguably more balanced than either of its individual components. With this motivation, we propose a new class of criteria for linear model selection based on targeting the symmetric divergence. Our criteria may be regarded as analogues of AIC and two of its variants: `corrected' AIC We examine the selection tendencies of the new criteria in a simulation study. Our results indicate that the new criteria perform favorably against their AIC analogues. Acknowledgments. The author is indebted to the editor, the associate editor, and two referees whose thoughtful suggestions helped to improve the original version of this manuscript.