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January, 1980 Adaptive Multivariate Ridge Regression
P. J. Brown, J. V. Zidek
Ann. Statist. 8(1): 64-74 (January, 1980). DOI: 10.1214/aos/1176344891


A multivariate version of the Hoerl-Kennard ridge regression rule is introduced. The choice from among a large class of possible generalizations is guided by Bayesian considerations; the result is implicitly in the work of Lindley and Smith although not actually derived there. The proposed rule, in a variety of equivalent forms is discussed and the choice of its ridge matrix considered. As well, adaptive multivariate ridge rules and closely related empirical Bayes procedures are presented, these being for the most part formal extensions of certain univariate rules. Included is the Efron-Morris multivariate version of the James-Stein estimator. By means of an appropriate generalization of a result of Morris (see Thisted) the mean square error of these adaptive and empirical Bayes rules are compared.


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P. J. Brown. J. V. Zidek. "Adaptive Multivariate Ridge Regression." Ann. Statist. 8 (1) 64 - 74, January, 1980.


Published: January, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0425.62053
MathSciNet: MR557554
Digital Object Identifier: 10.1214/aos/1176344891

Primary: 62J05
Secondary: 62C10 , 62C15 , 62C99 , 62H99

Keywords: Bayesian regression , Empirical Bayes , minimax , unbiased risk estimation

Rights: Copyright © 1980 Institute of Mathematical Statistics


Vol.8 • No. 1 • January, 1980
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