A Monte Carlo Evaluation of Some Ridge-Type Estimators

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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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