Generalized ridge estimator and model selection criteria in multivariate linear regression

We propose new model selection criteria based on generalized ridge estimators dominating the maximum likelihood estimator under the squared risk and the Kullback–Leibler risk in multivariate linear regression. Our model selection criteria have the following desirable properties: consistency, unbiasedness, and uniformly minimum variance. Consistency is proven under an asymptotic structure p∕n→c, where n is the sample size and p is the parameter dimension of the response variables. In particular, our proposed class of estimators dominates the maximum likelihood estimator under the squared risk, even when the model does not include the true model. Experimental results show that the risks of our model selection criteria are smaller than those based on the maximum likelihood estimator, and that our proposed criteria specify the true model under some conditions.