Some theoretical results for generalized ridge regression estimators

We examine some interpretations and theoretical properties of the ridge regression estimators. As such we (i) interpret the GRR estimator as an OLS one based on transformed explanatory variables; (ii) compare the GRR and OLS estimators using the confidence regions; (iii) prove the optimality of the OLS estimator for estimating the signs of the parameters;and (iv) compare the necessary and sufficient condition for the transformed explanatory variables to be less collinear than the initial ones with the condition for improving the OLS estimator.