A simulation study on strategic strata boundary determination using ranked set sampling technique

Convenient stratification criteria like nominal variables, encompassing natural conditions such as age, gender, etc., or geographical regions, don’t contribute significantly to enhancing the efficiency of estimates for the variables of interest. Therefore, it becomes imperative to devise an effective stratification framework that divides the entire population among heterogeneous strata, each homogeneous within itself, thereby achieving heightened accuracy in estimation. This study addresses the optimization of stratification methods using an auxiliary variable (X) within the context of the Neyman allocation under ranked set sampling. Specifically, the research focuses on scenarios where the regression function of the estimation variable (Y) on the X, when the variance \(V\left( {y|x} \right)\), is known. A \({\text{cum}}\sqrt[3]{{K_{2} (x)}}\) is proposed for approximating optimal strata boundaries. Furthermore, an empirical investigation is conducted and presented to illustrate the relative efficiency of the proposed methodology.