New AIC corrected variants for multivariate linear regression model selection

Estimation of the expected Kullback-Leibler information is the basis for deriving the Akaike information criterion (AIC) and its corrected version AIC_c. Both criteria were designed for selecting multivariate regression models with an appropriateness of AIC_c for small sample cases. In the work presented here, two new small sample AIC corrections are derived for multivariate regression model selection. The proposed AIC corrections are based on asymptotic approximation of bootstrap-type estimates of Kullback-Leibler information. These new corrections are of particular interest when the use of bootstrap is not really justified in terms of the required calculations. As it is the case for AIC_c, the new proposed criteria are asymptotically equivalent to AIC. Simulation results demonstrate that in small sample size settings, one of the proposed criterion provides better model choices than other available model selection criteria. As a result, this proposed criterion serves as an effective tool for selecting a model of appropriate order. Asymptotic justifications for the proposed criteria are provided in the Appendix.