Stein-type estimation using ranked set sampling

Abstract

In this study, we consider the application of the James–Stein estimator for population means from a class of arbitrary populations based on ranked set sample (RSS). We consider a basis for optimally combining sample information from several data sources. We succinctly develop the asymptotic theory of simultaneous estimation of several means for differing replications based on the well-defined shrinkage principle. We showcase that a shrinkage-type estimator will have, under quadratic loss, a substantial risk reduction relative to the classical estimator based on simple random sample and RSS. Asymptotic distributional quadratic biases and risks of the shrinkage estimators are derived and compared with those of the classical estimator. A simulation study is used to support the asymptotic result. An over-riding theme of this study is that the shrinkage estimation method provides a powerful extension of its traditional counterpart for non-normal populations. Finally, we will use a real data set to illustrate the computation of the proposed estimators.

Keywords:

• James–Stein estimator
• quadratic loss
• ranked set sampling
• restricted estimator
• shrinkage estimator
• simple random sampling

Acknowledgements

This work was supported by the King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia, under the internal project # IN/ 2008-413.