Optimal designs under the second-order least squares estimator:

MSc Thesis

Optimal regression design under second-order least squares estimator: theory, algorithm and applications

Author: Chi-Kuang Yeh

Supervisor: Julue Zhou

Abstract: In this thesis, we first review the current development of optimal regression designs under the second-order least squares estimator in the literature. The criteria include A- and D-optimality. We then introduce a new formulation of A-optimality criterion so the result can be extended to c-optimality which has not been studied before. Following Kiefer's equivalence results, we derive the optimality conditions for A-, c- and D-optimal designs under the second-order least squares estimator. In addition, we study the number of support points for various regression models including Peleg models, trigonometric models, regular and fractional polynomial models. A generalized scale invariance property for D-optimal designs is also explored. Furthermore, we discuss one computing algorithm to find optimal designs numerically. Several interesting applications are presented and related MATLAB code are provided in the thesis.

School: University of Victoria

Paper

Properties of optimal regression designs under the second-order least squares estimator

Software used

• This research was programmed on MATLAB, version 2016a. MATLAB can be downloaded from MathWorks.

• In addition, CVX version 2.1 was used.

Models

• Michaelis Menton Model (MM)
• Compartment Model
• Emax Model
• Polynomial model
• Fractional Polynomial model
• etc. ...