An iterative approach to variable selection based on the Kullback-Leibler information

Model selection criteria based on estimates of the Kullback-Leibler information have become popular among statisticians and econometricians. This group of criteria includes Akaike's (1973) AIC and Sugiura's (1978) bias corrected AIC (AIC_C). It has been suggested that reduction of the bias in estimating the Kullback-Leibler information can lead to better model selection. In this paper we propose a method of reducing the bias of AIC_C by relaxing one of the key assumptions made in its derivation. Monte Carlo evidence presented suggests that this new procedure outperforms AIC_C under certain circumstances even in very small samples. Despite this, the results indicate that AIC_c's model selection performance is highly robust to the assumption that is made.