New estimators in ranked set sampling in the presence of tie information

Ranked set sampling is a frequently used sampling method developed as an alternative to the simple random sampling. In this sampling method, rankers are expected to rank the units within the set correctly, even with low confidence. Also, if there are two or more very similar or identical units in a set, this makes ranking more difficult and it causes the units in the set to be ranked incorrectly. In this thesis, the mean estimators are examined under a method (RSS-t) in which the ranking error, occurred while ranking with the aid of the auxiliary variable, is reduced by using the tie information under the Ranked Set Sampling. The study aims to examine the ties in the ranking and to use these ties in the population mean estimators for more reliable estimates by minimizing the ranking error. After examining the method and the estimators in the literature, it is seen that the ratio estimators have not been examined under this method and therefore new modified raito estimators are proposed in this thesis study. The effectiveness of the estimators is first calculated for the samples drawn from large and small populations derived from simulation. Simulation studies have shown that the proposed estimators are more effective than other estimators in the literature. In addition, when the variables of the number of diagnosed patients and the number of patients who died are examined in a real data set of the recently emerging COVID-19 epidemic, it is seen that the data set is suitable for the tie information structure. Similar to the simulation results, we can also see from the real data set that the proposed estimators give better results.