Sankhya: The Indian Journal of Statistics
2005, Volume 67, Pt. 2, 295--304
Quantile Estimation from Ranked Set Sampling Data
Min Zhu, CSIRO Mathematical and
Information Sciences, Australia
You-Gan Wang, National University of Singapore and CSIRO, Floreat Park, Australia
SUMMARY. We consider estimation of quantiles when data are generated from ranked set sampling. A new estimator is proposed and is shown to have a smaller asymptotic variance for all distributions. It is also shown that the optimal sampling strategy is to select observations with one fixed rank from different ranked sets. Both the optimal rank and the relative efficiency gain with respect to simple random sampling are distribution-free and depend on the set size and the given probability only. In the case of median estimation, it is analytically shown that the optimal design is to select the median from each ranked set.
AMS (1991) subject classification. 62G32, 62G99.
Key words and phrases. Asymptotic variance, efficiency, optimal design, rank\-ed set sampling, quantile estimation.