The College of Administration and Economics at the University of Baghdad discussed , a master’s thesis in field of Statistics by the student (Zahraa Mohammed Mahmmod) and tagged with (Comparison Between Some Method of Estimating the Parameters of the Fractional Trigonometric Polynomial Regression Model With Application ) , Under supervision of ( Prof. Dr. Ahmed Dheyab Ahmed )
Nonlinear models have emerged as powerful tools that surpass the limitations of traditional linear models. Among these approaches, the fractional trigonometric polynomial regression model represents an advanced statistical technique that integrates the flexibility of polynomial functions with the precision of trigonometric terms in capturing nonlinear and periodic relationships within the data. This study aims to examine the fractional trigonometric polynomial regression model and compare several methods for estimating its parameters, namely Maximum Likelihood (ML), Fourier Analysis, Ordinary Least Squares (OLS), and two bootstrap approaches—Pairs Bootstrap and Residual Bootstrap. The comparison is conducted using the Mean Squared Error (MSE) criterion to identify the most accurate and efficient estimation method .
The experimental component of the study was carried out using MATLAB through simulation experiments with three sample sizes (30, 60, and 100). Meanwhile, the applied component involved analyzing real medical data of patients with diabetes and hypertension to evaluate the model’s predictive ability regarding the relationships among body mass, age, and levels of blood glucose or blood pressure. The findings indicate that the Maximum Likelihood (ML) method outperformed the other techniques, achieving the highest estimation accuracy and the lowest MSE value, making it the most suitable approach for parameter estimation in this model. The study recommends adopting this model when analyzing data that exhibit nonlinear and periodic patterns due to its superior flexibility and accuracy compared to traditional statistical models.
