An Investigation of the Probability Distribution of the Ridge Regression Estimator for Linear Models

The estimation of the parameters of a linear statistical model is generally accomplished by the method of least squares. However, when the method of least squares is applied to nonorthogonal problems the resulting estimates may be significantly different from the true parameters. The method of ridge regression may provide better estimates in these cases however, a probability distribution of the ridge estimator is presently not known. The form of such a distribution is dependent upon how the ridge parameter, k, is selected. Two possible objective methods of choosing k are examined to determine if either one leads to a useful probability distribution.