A Study on the Bias-Correction Effect of the AIC for Selecting Variables in Normal Multivariate Linear Regression Models Under Model Misspecification

Abstract

By numerically comparing a variable-selection method using the crude AIC with those using the bias-corrected AICs, we find out knowledge about what kind of bias correction gives a positive effect to variable selection under model misspecification. Actually, since all the variable-selection methods considered in this paper asymptotically choose the same model as the best model, we conduct numerical examinations using small and moderate sample sizes. Our results show that bias correction under assumption that the mean structure is misspecified gives a better effect to a variable-selection method than that under the assumption that the distribution of the model is misspecified.