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Journal of the American Statistical Association Volume 70, 1975 - Issue 350
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Theory and Method

A Monte Carlo Evaluation of Some Ridge-Type Estimators

Gary C. McDonald General Motors Research Laboratories, General Motors Technical Center, Warren, Mich., 48090, USA
&
Diane I. Galarneau General Motors Research Laboratories, General Motors Technical Center, Warren, Mich., 48090, USA
Pages 407-416 | Received 01 Feb 1973, Published online: 06 Apr 2012
 
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Abstract

Consider the standard linear model . Ridge regression, as viewed here, defines a class of estimators of indexed by a scalar parameter k. Two analytic methods of specifying k are proposed and evaluated in terms of mean square error by Monte Carlo simulations. With three explanatory variables and determined by the largest eigenvalue of the correlation matrix, least squares is dominated by these estimators in all cases investigated; however, mixed results are obtained with determined by the smallest eigenvalue. These estimators compare favorably with other ridge-type estimators evaluated elsewhere for two explanatory variables.

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