Xiaoqing Zhang

Topic

Numerical Construction of K-Optimal Designs for Linear, Nonlinear, and Generalized Linear Models

Department of Mathematics and Statistics

Date & location

• Friday, November 28, 2025
• 2:00 P.M.
• Virtual Defence

Examining Committee

Supervisory Committee

• Dr. Julie Zhou, Department of Mathematics and Statistics, University of Victoria (Supervisor)
• Dr. Min Tsao, Department of Mathematics and Statistics, UVic (Member)

External Examiner

• Dr. Po Yang, Department of Statistics, University of Manitoba

Chair of Oral Examination

• Dr. Daler Rakhmatov, Department of Electrical and Computer Engineering, UVic

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.