Quantiles naïve, ratio and difference estimators for efficient stratified sampling designs

This paper proposes and investigates the bivariate, the marginal distribution functions and quantiles estimators and their asymptotic properties for naïve, ratio, and difference estimators based on the bivariate stratified simple random sampling (BVSSRS) and bivariate stratified ranked set sampling designs (BVSRSS). We demonstrate that the proposed estimators using BVSRSS and BVSSRS are consistent and asymptotically normally distributed. Improved performance of the proposed estimators using BVSRSS compared to BVSSRS supported through an intensive simulation study. The derivation of the optimal allocation based on BVSSRS and BVSRSS is provided. The National Health and Nutrition Examination Survey (NHANES) data is used to illustrate the methods.