Quantile Estimation Using Ranked Set Samples from a Population with Known Mean

Abstract

Ranked set sampling (RSS) is a cost-efficient technique for data collection when the units in a population can be easily judgment ranked by any cheap method other than actual measurements. Using auxiliary information in developing statistical procedures for inference about different population characteristics is a well-known approach. In this work, we deal with quantile estimation from a population with known mean when data are obtained according to RSS scheme. Through the simple device of mean-correction (subtract off the sample mean and add on the known population mean), a modified estimator is constructed from the standard quantile estimator. Asymptotic normality of the new estimator and its asymptotic efficiency relative to the original estimator are derived. Simulation results for several underlying distributions show that the proposed estimator is more efficient than the traditional one.

Keywords:

• Mean-correction
• Quantile estimation
• Ranked set sampling

2000 Mathematics Subject Classification:

• 62G30
• 62G99

Acknowledgement

We would like to thank the anonymous referees and the Associate Editor for providing helpful comments that greatly improved the initial version of this article.