Abstract
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.
Citation
Isamu Nagai. Hirokazu Yanagihara. Kenichi Satoh. "Optimization of ridge parameters in multivariate generalized ridge regression by plug-in methods." Hiroshima Math. J. 42 (3) 301 - 324, November 2012. https://doi.org/10.32917/hmj/1355238371
Information