SEPARATE VERSUS SYSTEM METHODS OF STEIN-RULE ESTIMATION IN SEEMINGLY UNRELATED REGRESSION MODELS

ABSTRACT

Despite the sizeable literature associated with the seemingly unrelated regression models, not much is known about the use of Stein-rule estimators in these models. This gap is remedied in this paper, in which two families of Stein-rule estimators in seemingly unrelated regression equations are presented and their large sample asymptotic properties explored and evaluated. One family of estimators uses a shrinkage factor obtained solely from the equation under study while the other has a shrinkage factor based on all the equations of the model. Using a quadratic loss measure and Monte-Carlo sampling experiments, the finite sample risk performance of these estimators is also evaluated and compared with the traditional feasible generalized least squares estimator.

Keywords:

• Bias
• Large sample asymptotic
• Quadratic loss
• Risk
• Mean squared error
• Monte-Carlo simulation
• Seemingly unrelated regression

ACKNOWLEDGMENTS

Much of the early work on this paper was carried out during the first author's last overseas visit to Hong Kong in July 2000 before he was diagnosed with prostate cancer. The second author wishes to thank Anoop Chaturvedi, Shalabh, Aman Ullah, Guohua Zou and two anonymous referees for many helpful comments that have considerably improved the paper. Financial support from the City University of Hong Kong is also gratefully acknowledged.