The College of Administration and Economics at the University of Baghdad discussed, a PhD dissertation in field of Statistics by the student (Huda Yahya Ahmed) and tagged with (Estimation of Multivariate Partially Linear Models with Application ) , Under supervision of (Assist.Prof. Dr.Emad Hazim Aboudi )
this dissertation addresses the estimation of the Multivariate Partially Linear Model (MPLM), which combines a linear parametric component with a nonlinear nonparametric component. The research problem arises from the presence of multiple correlated response variables and a nonlinear structure, making the estimation process more challenging.
To tackle this issue, this dissertation develops a semi-parametric estimation framework and provides a comprehensive comparison of several advanced estimation methods, including Profile Least Squares, Profile Likelihood, and Two-Stage Local Linear Estimation. Additionally, Kernel and Spline techniques are employed as smoothing methods for the nonparametric component. Furthermore, Copula-based methods are incorporated as a flexible approach to model the dependence structure among multivariate responses, as they effectively capture nonlinear dependence beyond traditional variance–covariance approaches.
The performance of the proposed methods is evaluated through simulation studies under different sample sizes, varying correlation levels, and diverse variance–covariance structures, using Mean Squared Error (MSE) as the evaluation criterion. In addition, the methodologies are applied to real groundwater quality data from Baghdad Governorate, consisting of 36 wells distributed across Abu Ghraib and Al-Mahmoudiya regions. The analysis examines the effects of total dissolved solids and major ions on groundwater quality indicators, contributing to the assessment of water suitability for domestic, agricultural, and industrial uses.
The results from both simulation and real data applications indicate that Copula-based methods combined with spline smoothing (Copula + Spline) achieve the lowest MSE values in most scenarios, particularly under high correlation among response variables. This demonstrates their superior capability in modeling complex dependence structures and improving estimation and prediction accuracy compared to alternative methods.
Overall, this dissertation provides a robust applied statistical framework for groundwater quality assessment, water resource management, and environmental decision-making. Moreover, the proposed approach is applicable to other fields requiring flexible multivariate modeling, such as public health, economics, and engineering, thereby enhancing statistical inference and supporting informed decision-making under complex dependency structures.
