Bayesian interpretation of some biased estimators in lineer regression

The Bayes estimator and biased estimators are discovered by different researchers quite independently. A careful study of the literature shows that these estimators have many similarities. Moreover, these estimators frequently have smaller mean square error than the least square estimator. This result is found to be very useful in the analysis of multicollinear data. Rao (1971) derives the ridge estimator as a special case of the Bayes estimator. A comprehensive presentation of the Bayesian interpretation of the Stein-rule estimator is given by Vinod and Ullah (1981). This study primarily deals with analyzing the relationship between some biased regression estimators and the Bayes estimator. Modified ridge estimator, restricted ridge estimator, Liu estimator, adaptive optimal estimator and two parameter estimator are discussed from a Bayesian point of view. Various biased estimators related to the Bayes estimator are compared theoretically according to some criteria. The results are supported by numerical example and Monte Carlo simulation.