Optimal regression design under second-order least squares estimator: theory, algorithm and applications
Date
2018-07-23
Authors
Yeh, Chi-Kuang
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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.
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Keywords
Optimal design, Statistics, Second-order least squares estimator, Convex optimization, Generalized scale invariance, Number of support points