AN EXPANSION OF THE GENERALIZED RIDGE ESTIMATOR IN A LINEAR REGRESSION MODEL

Abstract

In a linear regression model, it was shown by Hoerl and Kennard (1970a) that the generalized Ridge estimator has “potentially” smaller Mean Squared Error (MSE) as an alternative to the Ordinary Least Squares (OLS) estimator.
In this paper, we apply this estimator in a problem predicting a future objective variable on a prediction area different from a sample area, and we extend the generalized Ridge estimator with respect to the axes (column vectors of an orthogonal transformation matrix) on which we shrink with a diagonal matrix. A goodness of estimator is evaluated in the expectation of Prediction Mean Squared Error with respect to the future sample point.