Further results on the generalized Liu-type estimators under the balanced loss function

Abstract

In regression analysis, ridge regression estimators and Liu type estimators are often used to overcome the collinearity problem. 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 effciency of an estimator only takes the error of estimation into account. In 1994, Zellner proposed a balanced loss function. Recently, Akdeniz et al. (6) considered the balanced loss function which incorporates a measure for the goodness of fit of the model as well as the precision of estimation in the evaluation of the feasible generalized Liu estimator (FGLE) and almost unbiased feasible generalized Liu estimator (AUFGLE). In this paper, we derive, numerically evaluate and compare the risks of the FGLE and AUFGLE for four different degrees of multicollinearity under the balanced loss function.