Numerical construction of K-optimal designs for linear, nonlinear, and generalized linear models
| dc.contributor.author | Zhang, Xiaoqing | |
| dc.contributor.supervisor | Zhou, Julie | |
| dc.date.accessioned | 2025-12-09T21:24:53Z | |
| dc.date.available | 2025-12-09T21:24:53Z | |
| dc.date.issued | 2025 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science MSc | |
| dc.description.abstract | This thesis investigates the numerical construction of K-optimal designs for a variety of statistical models. These include linear models such as polynomial, trigonometric, and second-order response models, nonlinear models such as Michaelis–Menten, compartmental, and Peleg models, and generalized linear models with a particular focus on logistic regression. K-optimality aims to minimize the condition number of the Fisher information matrix to improve the numerical stability in parameter estimation. A general algorithm is proposed and applied to all models to construct K-optimal designs, evaluated under different design spaces and parameter values. For nonlinear models, the K-optimal designs are compared with A-optimal and D-optimal designs, while for the logistic regression model, comparisons are made with D-optimal designs. The results show that K-optimal designs have stable patterns between different models. Factors such as design space, model type, and parameter values influence the support points, their weights, and the condition number. In addition, K-optimal designs achieve smaller condition numbers, indicating better numerical stability, and take less computation time than both D-optimal and A-optimal designs. All key findings are presented in tables and figures, and the MATLAB code used for the computations is provided in the thesis. | |
| dc.description.scholarlevel | Graduate | |
| dc.identifier.uri | https://hdl.handle.net/1828/22964 | |
| dc.language | English | eng |
| dc.language.iso | en | |
| dc.rights | Available to the World Wide Web | |
| dc.subject | Optimal design | |
| dc.subject | K-optimal design | |
| dc.title | Numerical construction of K-optimal designs for linear, nonlinear, and generalized linear models | |
| dc.type | Thesis |