基于广义排序集样本的分位数估计

为提高总体分位数的估计效率,提出基于广义排序集抽样的非参数加权估计量.根据估计量的强相合性和渐近正态性,给出了在任意给定的抽样方案下使渐近方差达到最小的权数.再利用最优权数的适应任意分布性,证明出使估计效率达到最大的抽样方案是从所有排序小组中挑选具有同一次序的观测值.通过对渐近相对效率的数值计算和一组真实数据的实际应用,表明最优加权估计功效高于无权估计,最优排序集抽样效率高于标准排序集抽样和简单随机抽样. 

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.