Two-Stage Cluster Sampling with Ranked Set Sampling in the Secondary Sampling Frame

Abstract

Motivated by a real-life problem, we develop a Two-Stage Cluster Sampling with Ranked Set Sampling (TSCRSS) design in the second stage for which we derive an unbiased estimator of population mean and its variance. An unbiased estimator of the variance of mean estimator is also derived. It is proved that the TSCRSS is more efficient—in the sense of having smaller variance—than the conventional two-stage cluster simple random sampling in which the second-stage sampling is with replacement. Using a simulation study on a real-life population, we show that the TSCRSS is more efficient than the conventional two-stage cluster sampling when simple random sampling without replacement is used in both stages.

Keywords:

• Ranked set sampling
• Simple random sampling
• Two-stage sampling
• Unbiased estimator
• Variance estimation

Mathematics Subject Classification:

• Primary 62D05
• Secondary 62F10

Acknowledgments

The authors would like to thank the Associate Editor and two anonymous referees for their helpful comments. Research of the first author was supported by the research council of Allameh Tabataba'i University and the work of second author was partially supported by the CEAMA of Isfahan University of Technology.