College of Computer Science and Mathematics

Discussion of the master’s thesis in the College of Computer Science and Mathematics -Department of Statistics and Informatics Department entitled:” The robust estimation of finite population mean for modified regression line by stratified ranked set sampling ”

Master’s thesis by  Ayman Mahmoud Khalaf

supervised by  Dr. Rikan Abdulazeez Ahmed

This thesis includes the presents and studies proposed estimators based on regression (separate and joint) to estimate the mean of a finite population within the framework of the stratified random sampling (S_t MRSS). These estimators are compared with regression estimators (separate and joint) for estimating the mean of the population in the context of stratified simple random sampling (S_t SRS), using robust methods in addition to traditional estimators, through the Mean Squared Error (MSE) criterion. Furthermore, the properties and efficiency of the proposed estimators are studied in comparison to previous counterparts to demonstrate their accuracy in representing the mean of the finite population.

The study addressed that using the stratified random sampling method (S_t MRSS) significantly improved the quality of regression estimators (separate and joint) for the population mean by reducing the influence of outliers. This was demonstrated through comparisons with various robust regression techniques (Huber M, Huber MM, LMS, LTS) and robust covariance matrices (MCD, MVE) in a simulation study. Results showed that the estimator from S_t MRSS outperformed others, especially in joint regression, across different sample sizes (n = 100, 250, 400, 500) and varying outlier proportions (10%, 15%, 20%, 25%), based on Mean Squared Error (MSE) and Relative Efficiency (RE). The theoretical results were applied to real data from the Nineveh Agricultural Directorate to estimate the average expected wheat yield for Nineveh Province.

The study aims to estimate the mean of a finite population using proposed estimators for separate and combined regression (Regression Combined-Separate estimates) based on the stratified random sampling method (S_t MRSS). It also employs robust methods for estimating regression parameters, including Huber M, Huber MM, LTS, and LMS, along with robust covariance matrices (MCD, MVE).

The discussion committee consists of

(Chairman)   Dr. Raya Salem Muhammad Ali

(member)     Dr. Bashar Abdul Aziz Majid

(Member)    Dr. Noursel Ahmed Zain Al-Abidin

(member and supervisor)      Dr. Rikan Abdulazeez Ahmed