Asymptotic bootstrap corrections of AIC for linear regression models

The Akaike information criterion, AIC, and its corrected version, AIC_c are two methods for selecting normal linear regression models. Both criteria were designed as estimators of the expected Kullback-Leibler information between the model generating the data and the approximating candidate model. In this paper, two new corrected variants of AIC are derived for the purpose of small sample linear regression model selection. The proposed variants of AIC are based on asymptotic approximation of bootstrap type estimates of Kullback-Leibler information. These new variants are of particular interest when the use of bootstrap is not really justified in terms of the required calculations. As its the case for AIC_c, these new variants are asymptotically equivalent to AIC. Simulation results which illustrate better performance of the proposed AIC corrections when applied to polynomial regression in comparison to AIC, AIC_c and other criteria are presented. Asymptotic justifications for the proposed criteria are provided in the Appendix.