On Kernel-based Quantile Estimation Using Different Stratified Sampling Schemes With Optimal Allocation

The kernel-based estimators of a quantile function based on stratified samples of simple random sampling and ranked set sampling methods are proposed. The expectations and variances of the estimators are analytically obtained as well as their asymptotic distributions. Effect of imperfect ranking is considered in all analytically and numerically results. As theory and using a simulation study, it is shown that the estimator based on stratified ranked set sampling is more efficient than its counterpart on the basis of stratified simple random sampling. The simulation study is performed for three strata with small samples as well as large samples and for ten strata. Finally, the performance of the estimator is investigated by using China Health and Nutrition data set.