Ridge Estimation in Linear Regression.

Abstract

Consider the linear regression model Y = X Theta + epsilon. Recently, a class of estimators, variously known as ridge estimators, has been proposed as an alternative to the least squares estimators in the case of collinearity, that is, when the design matrix X'X is nearly singular. The ridge estimator is given by Theta-cap = (1/(X'X + KI)) X'Y, where K is a constant to be determined. An optimal choice of the value of K is not known. This paper examines the risk (mean squared error) of the ridge estimator under the constraint Theta'Theta < r or = c and determines optimal values of K for which the risk is smaller than the risk of the least squares estimators where c is a constant. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1976
Accession Number
ADA083521

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  • James S. Hawkes

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  • Clemson University

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