The weighted average information criterion for multivariate regression model selection

We propose a consistent criterion WIC _vc (vector corrected weighed average information criterion) for model order selection in multivariate linear regression models. The WIC _vc is a weighted average of the asymptotically efficient criterion KIC _vc (vector corrected Kullback information criterion) and the consistent criterion MBIC (multivariate Bayesian information criterion). The WIC _vc behaves like KIC _vc in small samples and behaves like MBIC in large samples. A numerical study comparing the performance of the proposed criterion with several available model selection criteria has been done. It shows that, over a wide range of small, moderate and large sample sizes, the WIC _vc is more stable in comparison to other criteria in the study; that is, the WIC _vc is either as good or comes in a strong second, whereas other criteria vary more in performance ranking. Therefore, the WIC _vc is a very reliable and practical criterion.