The Mean Squared Error of the Generalized Ridge Regression Estimator and the Orientation of β

Newhouse and Oman (1971) identified the orientations with respect to the eigenvectors of X'X of the true coefficient vector of the linear regression model for which the ordinary ridge regression estimator performs best and performs worse when mean squared error is the measure of performance. In this paper the corresponding result is derived for generalized ridge regression for two risk functions: mean squared error and mean squared error of prediction.