Information theory approach to ranked set sampling and new sub-ratio estimators

In this study, we introduce a new approach to the mean estimators in ranked set sampling. The amount of information carried by the auxiliary variable is measured with the Shannon entropy method on populations and samples and to use this information in the estimator, the basic ratio and the generalized exponential ratio estimators are modified as sub-ratio estimators to use only the information on the sample. Without using the required population parameter for ratio estimators, we propose new sub-ratio type estimators using only the auxiliary variable for ranking in the implementation of the ranked set sampling method. The mean squared errors and bias formulas of the proposed estimators are obtained and it is shown that the proposed estimators are more efficient than the classic mean estimator and ratio estimator of RSS under the certain theoretical conditions. Simulation and real data studies also show that the proposed estimators always give better results than the mean estimators of ranked set sampling and it is observed that the relative efficiencies of the proposed estimators increase depending on the magnitude of the entropy, the correlation between the auxiliary and the study variables, and the set sizes.