Multivariate regression model selection from small samples using Kullback's symmetric divergence

The Kullback Information Criterion, KIC, and its univariate bias-corrected version, KIC_c, are two new developed criteria for model selection. The two criteria can be viewed as estimators of the expected Kullback symmetric divergence and they have a fixed bias corrected term. In this paper, a new small sample model selection criterion for multivariate regression models is developed. The proposed criterion is named KIC_vc, where the notation "vc" stands for vector correction, and it can be considered as an extension of KIC for multivariate regression models. KIC_vc adjusts KIC to be an unbiased estimator for the variant of the Kullback symmetric divergence, assuming that the true model is correctly specified or overfitted. Furthermore, KIC_vc provides better multivariate regression model order or dimension choices than KIC in small samples. Simulation results shows that the proposed criterion estimates the model order more accurately than other asymptotically efficient methods when applied to multivariate regression model selection in small samples. As a result, KIC_vc serves as an effective tool for selecting a multivariate regression model of appropriate dimension. A theoretical justification of the proposed criterion is presented.