On Quantiles Estimation Based on Different Stratified Sampling with Optimal Allocation

In this work, we consider the problem of estimating a quantile function based on different stratified sampling mechanisms. First, we develop an estimate for population quantiles based on stratified simple random sampling (SSRS) and extend the discussion for stratified ranked set sampling (SRSS). We also study the asymptotic behavior of the proposed estimators. Here, we derive an analytical expression for the optimal allocation under both sampling schemes. Simulation studies are designed to examine the performance of the proposed estimators under varying distributional assumptions. The efficiency of the proposed estimates is further illustrated by analyzing a real data set containing TC biomarker values taken from 10,187 Chinese children and adults (>age 7) in the year 2009.