Generalized Liu Type Estimators Under Zellner's Balanced Loss Function

Abstract

ABSTRACT In regression analysis, ridge regression estimators and Liu type estimators are often used to overcome the problem of multicollinearity. These estimators have been evaluated using the risk under quadratic loss criterion, which places sole emphasis on estimators′ precision. The traditional mean square error (MSE) as the measure of efficiency of an estimator only takes the error of estimation into account. In 1994, Zellner proposed a balanced loss function. Here, we consider the balanced loss function which incorporates a measure for the goodness of fit of the model as well as estimation precision. We also examine the risk performance of the feasible generalized Liu estimator and feasible almost unbiased generalized Liu estimator when the balanced loss function is used.