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

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.

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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

Published: November 2012
First available in Project Euclid: 11 December 2012

zbMATH: 1257.62081
MathSciNet: MR3050124
Digital Object Identifier: 10.32917/hmj/1355238371

Subjects:
Primary: 62J07
Secondary: 62H12

Rights: Copyright © 2012 Hiroshima University, Mathematics Program

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Vol.42 • No. 3 • November 2012
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