Multivariate regression model selection with KIC for extrapolation cases

The Kullback information criterion, KIC and its multivariate bias-corrected version, KIC_VC are two alternatively developed criteria for model selection. The two criteria can be viewed as estimators of the expected Kullback symmetric divergence. In this paper, a new criterion is proposed in order to select a well fitted model for an extrapolation case. The proposed criterion is named, PKIC, where "P" stands for prediction, and is derived as an exact unbiased estimator of an adapted cost function that is based on the Kullback symmetric divergence and the future design matrix. PKIC is an unbiased estimator of its cost function assuming that the true model is correctly specified or overfitted. A simulation study illustrating that model selection with PKIC performs well for some extrapolation cases is presented.