Affiliations: [a] Department of Statistics, Gazi University, Teknikokullar, 06500 Ankara, Turkey | [b] Department of Statistics, Çukurova University, 01330 Adana, Turkey | [c] Department of Management Sciences, City University of Hong Kong, Tat Che Avenue, Kowlon, Hong Kong | [d] Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
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.
Keywords: Balanced loss, collinearity, Liu estimator, loss function, ridge estimator, risk function