Ridge Estimation in Linear Regression.

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 XX is nearly singular. The ridge estimator is given by Theta-cap 1XX KI XY, 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 ThetaTheta 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