The College of Administration and Economics at the University of Baghdad discussed , a master’s thesis in field of Statistics by the student (Mohammad Adel Kazem) and tagged with (Comparison of Some Calibration Estimators for Estimating the Population Mean in Stratified Random Sampling with Application) , Under supervision of (Assist. Prof. Dr. Saja Mohammad Hussein ).
Sampling methods are considered fundamental tools in scientific research, as they enable researchers to study the characteristics of a statistical population with precision and efficiency. Stratified random sampling is one of the most prominent probabilistic methods used in statistical studies due to its role in enhancing the accuracy of estimates. In stratified random sampling, estimating the population mean is of great importance in many studies, and various estimation approaches exist for this purpose. Among these approaches is the calibration technique, which aims to adjust sample weights by minimizing a distance function between the original and adjusted weights, subject to a set of constraints related to auxiliary information. The new weights are determined using the Lagrange multiplier method, ensuring they remain close to the original weights.
In this thesis, the population mean under stratified random sampling was estimated using a single auxiliary variable based on several calibration estimators. The population mean variance was also estimated, and the performance of these estimators was compared in terms of efficiency and accuracy using the Mean Squared Error (MSE) as the primary comparison criterion, along with Relative Efficiency (RE).
The study included an experimental component using simulated data following a normal distribution to evaluate the efficiency of calibration estimators in estimating the population mean, as well as an applied component based on real data of wheat production in Iraq for the year 2023. The results showed that all calibration estimators outperformed the traditional Cochran estimator. Among them, the Koyuncu and Kadilar estimator proved to be the best, achieving the lowest MSE values and the highest relative efficiency across all cases—reaching RE = 650% for simulated data and RE = 983% for real data. These exceptionally high relative efficiency values indicate that using the calibration approach in stratified random sampling significantly improves estimation accuracy compared to the traditional method.
The conclusions and recommendations derived from the study emphasize that employing the calibration technique in stratified random sampling is an effective approach to improving the precision of estimates. It is recommended to apply this technique in official statistical studies, especially in agricultural and economic fields, as it provides high efficiency in utilizing auxiliary information and enhances estimation accuracy.
