https://github.com/chikuang/optimaldesigns-slse
MATLAB code for finding optimal designs using the second-order least squares estimation
https://github.com/chikuang/optimaldesigns-slse
optimal-designs statistics
Last synced: 8 months ago
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MATLAB code for finding optimal designs using the second-order least squares estimation
- Host: GitHub
- URL: https://github.com/chikuang/optimaldesigns-slse
- Owner: chikuang
- Created: 2017-09-27T20:06:35.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2024-05-14T01:31:56.000Z (about 2 years ago)
- Last Synced: 2025-10-12T00:54:16.486Z (9 months ago)
- Topics: optimal-designs, statistics
- Language: MATLAB
- Homepage:
- Size: 422 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Optimal designs under the second-order least squares estimator:
### MSc Thesis
[Optimal regression design under second-order least squares estimator: theory, algorithm and applications](https://dspace.library.uvic.ca/handle/1828/9765)
Author: [Chi-Kuang Yeh](http://www.math.uvic.ca/~chikuang/)
Supervisor: [Julue Zhou](http://www.math.uvic.ca/~jzhou/)
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](https://www.uvic.ca/)
### Paper
[Properties of optimal regression designs under the second-order least squares estimator](https://link.springer.com/article/10.1007%2Fs00362-018-01076-6)
### Software used
* This research was programmed on MATLAB, version 2016a. MATLAB can be downloaded from [MathWorks](https://www.mathworks.com/products/matlab.html).
* In addition, [CVX](http://cvxr.com/cvx/) version 2.1 was used.
### Models
* Michaelis Menton Model (MM)
* Compartment Model
* Emax Model
* Polynomial model
* Fractional Polynomial model
* etc. ...