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Optimization of ridge parameters in multivariate generalized ridge regression by plug-in methods. (English) Zbl 1257.62081
Summary: Generalized ridge (GR) regression for an univariate linear model was proposed simultaneously with ridge regression by A.E. Hoerl and R.W. Kennard [Technometrics 12, 55–67 (1970: Zbl 0202.17205)]. 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.

##### MSC:
 62J07 Ridge regression; shrinkage estimators (Lasso) 62H12 Estimation in multivariate analysis 65C60 Computational problems in statistics (MSC2010)
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