Generalized ridge regression and a generalization of the C_P statistic

We consider a generalization of ridge regression and demonstrate advantages over ridge regression. We provide an empirical Bayes method for determining the ridge constants, using the Bayesian interpretation of ridge estimators, and show that this coincides with a method based on a generalization of the C_P statistic and the non-negative garrote. These provide an automatic variable selection procedure for the canonical variables.