A Comparison of Ridge Estimators

Abstract

Least squares estimates of the parameters in the usual linear regression model are likely to be too large in absolute value and possibly of the wrong sign when the vectors of explanatory variables are multicollinear. Hoer1 and Kennard have demonstrated that these undesirable effects of multicollinearity can be reduced by using “ridge” estimates in place of the least squares estimates. Unfortunately, ordinary ridge estimates depend on a value, k, which, in practice, is determined by the data. Several mechanical rules and a graphical procedure, known as the ridge trace, have been proposed for selecting k.

In this paper we evaluate the relative performances of several mechanical selection rules, the ridge trace and the least squares procedure using computer simulation experiments.

KEY WORDS:

• Linear regression model
• Ridge estimator
• Ridge trace
• Mean square error