Some ratio estimators of finite population variance using auxiliary information in ranked set sampling

The method of selecting or designing the sample may be expensive or take a long time in some studies. And with the existence of the relationship between the main and auxiliary variables, which can employ in the process of selecting sampling units through the possibility of ranking for the auxiliary variable at the lowest possible cost. Ranked set sampling (\textit{RSS}) is a method to achieve this objective, and in sample surveys, it is usual to use auxiliary information to increase the precision of estimators. This article addresses the problem of estimating the finite population variance in ranked set sampling using auxiliary information, and that is through some suggested estimators. The bias and mean squared error of the proposed estimators are obtained up to the first degree of approximation. An asymptotic optimum estimator is identified with its approximate mean squared error (\textit{MSE}) formula. An estimator based on ``estimated optimum values'' is also investigated. Some special cases of these estimators are considered and compared using computer simulation. Finally, we showed how to extend the proposed estimator if more than one auxiliary variable is available.