Tabakalı Uç Sıralı Küme Örneklemesi Yönteminde Kitle Ortalamasının Kalibrasyon Tahmin Edicileri

Abstract

Stratified simple random sampling is one of the most frequently used sampling techniques in research. However, in cases where the population is very large and it is difficult to measure the sample units, but it is easier to rank them, the stratified ranked set sampling design is preferred. In the literature, stratified median, extreme, percentile and quartile ranked set sampling design have been proposed as alternatives to the stratified ranked set sampling design. Within the scope of the thesis, the "stratified extreme ranked set sampling" design is used and introduced. The reason why this sampling design is preferred is that, while in ranked set sampling the relevant ranked statistic from each set is selected without error, in extreme ranked set sampling it is sufficient to accurately determine only the smallest and largest ranked statistics. In this case, it is a more preferable design in terms of time and cost since it can be applied to large masses. In recent years, many studies have been carried out on stratified extreme ranked set sampling design, proposing various estimators for population mean estimation. Calibration estimation, which uses auxiliary information in the study variable to increase the precision and accuracy of population parameter estimators in sampling studies, is a widely used technique in statistics. In the thesis study, primarily stratified simple random sampling, stratified ranked set sampling and stratified extreme ranked set sampling designs and classical estimators were introduced, and then calibration estimators proposed by various authors were examined. In this thesis study, a new calibration estimator is proposed under new constraints for estimating the population mean in the stratified extreme ranked set sampling design. A simulation study was conducted to compare the proposed estimator with the calibration estimators existing in the literature in terms of effectiveness. For the simulation study, mean square error and relative efficiency values were calculated for different sample sizes, considering both real data and synthetic data. According to the results obtained, it was found that the calibration estimators proposed in the stratified extreme ranked set sampling in both data sets were more effective than the calibration estimators proposed in the stratified simple random sampling design.