A novel AIC variant for linear regression models based on a bootstrap correction

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, a new corrected variants of AIC is derived for the purpose of small sample linear regression model selection. The new proposed variant of AIC is based on asymptotic approximation of bootstrap type estimates of Kullback-Leibler information. Simulation results which illustrate better performance of the proposed AIC correction when applied to polynomial regression in comparison to AIC, AIC_c and other criteria are presented. Asymptotic justifications for the proposed criterion are provided in the Appendix.