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The General Expressions for the Moments of the Stochastic Shrinkage Parameters of the Liu Type Estimator |
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| Authors: | Fikri Akdeniz George P. H. Styan Hans Joachim Werner |
| Affiliation: | 1. Department of Statistics, Faculty of Arts and Sciences , University of ?ukurova , Adana, Turkey akdeniz@mail.cukurova.edu.tr;3. Department of Mathematics and Statistics , McGill University , Montreal, Quebec, Canada;4. Department of Statistics, Faculty of Economics , University of Bonn , Bonn, Germany |
| Abstract: | ABSTRACT One of the problems with the Liu estimator is the appropriate value for the unknown biasing parameter d. In this article we consider the optimum value for d and give upper bound for the expected value of the estimator of this biasing parameter. We also derive the general expressions for the moments of the stochastic shrinkage parameters of the Liu estimator and the generalized Liu estimator. Numerical calculations are carried out to illustrate the behavior of the mean and variance of the biasing parameter. Also, a numerical example is given to illustrate the effect of the biasing parameter d, on the mean square error of the Liu estimator. |
| Keywords: | Hypergeometric function Least squares estimator Liu estimator Moment Multicollinearty |