The weighted average information criterion for multivariate regression model selection

We propose a consistent criterion WICvc (vector corrected weighed average information criterion) for model order selection in multivariate linear regression models. The WICvc is a weighted average of the asymptotically efficient criterion KICvc (vector corrected Kullback information criterion) and the consistent criterion MBIC (multivariate Bayesian information criterion). The WICvc behaves like KICvc 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 WICvc is more stable in comparison to other criteria in the study; that is, the WICvc is either as good or comes in a strong second, whereas other criteria vary more in performance ranking. Therefore, the WICvc is a very reliable and practical criterion.

► A consistent model selection criterion WICvc in multivariate linear regression is proposed.
► The WICvc behaves like KICvc in small samples and behaves like MBIC in large samples.
► Studies show that, over a wide range of sample sizes, WICvc is more stable than other criteria.
► An example on tobacco leaf for organic and inorganic chemical constituents is analyzed by WICvc.