ABSTRACT This paper considers a Kullback-Leibler distance (KLD) which is asymptotically equivalent to the KLD by Goutis and Robert  when the reference model (in comparison to a competing fitted model) is correctly specified and that certain regularity conditions hold true (ref. Akaike ). We derive the asymptotic property of this Goutis-Robert-Akaike KLD under certain regularity conditions. We also examine the impact of this asymptotic property when the regularity conditions are partially satisfied. Furthermore, the connection between the Goutis-Robert-Akaike KLD and a weighted posterior predictive p-value (WPPP) is established. Finally, both the Goutis-Robert-Akaike KLD and WPPP are applied to compare models using various simulated examples as well as two cohort studies of diabetes.
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