A semiparametric generalized ridge estimator and link with model averaging

In recent years, the suggestion of combining models as an alternative to selecting a single model from a frequentist prospective has been advanced in a number of studies. In this article, we propose a new semiparametric estimator of regression coefficients, which is in the form of a feasible generalized ridge estimator by Hoerl and Kennard (1970b) but with different biasing factors. We prove that after reparameterization such that the regressors are orthogonal, the generalized ridge estimator is algebraically identical to the model average estimator. Further, the biasing factors that determine the properties of both the generalized ridge and semiparametric estimators are directly linked to the weights used in model averaging. These are interesting results for the interpretations and applications of both semiparametric and ridge estimators. Furthermore, we demonstrate that these estimators based on model averaging weights can have properties superior to the well-known feasible generalized ridge estimator in a large region of the parameter space. Two empirical examples are presented.