Pusat Pengajian Sains Matematik - Tesis

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Modified Iterative And Repetitive Estimation Methods For Fitting Measurement Error Model
(2025-03)
Al-Dibi’I, Ro’Ya Saleh Faleh
This thesis introduces new estimation methods for fitting structural measurement error model (mem), addressing challenges in estimating relationships where all variables are subject to error. The study focuses on distribution-free weighted estimation techniques, which improve parameter estimation without the strict assumptions required by traditional methods. A new weighted wald-type estimation procedure, developed in modified iterative and repetitive forms, is proposed and tested on both simple and multiple mems. Simulation studies show that these methods achieve lower mean square errors across various weighting scenarios, outperforming classical approaches such as maximum likelihood estimation (mle) and the method of moments (mom) in terms of accuracy and reliability. Additionally, robust weighted estimation methods, including theil and siegel procedures, demonstrate superior performance in different settings. The proposed techniques are applied to two real datasets: one examining the relationship between infant deaths, hepatitis b, and polio, revealing strong negative correlations, and another analyzing gross domestic product (gdp), unemployment, and the human development index (hdi) in jordan, highlighting strong positive correlations between gdp and hdi and a strong negative relationship between unemployment and hdi.