Estimation of Quantile Under General Ranked Set Sampling

To improve the estimation efficiency of the population quantile, a nonparametric weighted estimator under general ranked set sampling is proposed. According to the strong consistency and asymptotic normality of the proposed estimator, the weight that minimizes the asymptotic variance is identified for any given sampling scheme. By using the property that the optimal weight is distribution-free, it could be verified that the sampling allocation that maximizes the estimation efficiency is to select observation with one fixed rank from different ranked sets. The computational results of asymptotic relative efficiencies and a practical application to a real data set show that the efficiency of the optimal weighted estimator is higher than the un-weighted version, and the optimal ranked set sampling is more efficient than the standard ranked set sampling or the simple random sampling.