Optimization of ridge parameters in multivariate generalized ridge regression by plug-in methods

Generalized ridge (GR) regression for an univariate linear model was proposed simultaneously with ridge regression by Hoerl and Kennard (1970). In this paper, we deal with a GR regression for a multivariate linear model, referred to as a multivariate GR (MGR) regression. From the viewpoint of reducing the mean squared error (MSE) of a predicted value, many authors have proposed several GR estimators consisting of ridge parameters optimized by non-iterative methods. By expanding their optimizations of ridge parameters to the multiple response case, we derive some MGR estimators with ridge parameters optimized by the plug-in method. We analytically compare obtained MGR estimators with existing MGR estimators, and numerical studies are also given for an illustration.