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

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dc.contributor.authorYeh, Chi-Kuang
dc.contributor.supervisorZhou, Julie
dc.date.accessioned2018-07-23T22:20:08Z
dc.date.available2018-07-23T22:20:08Z
dc.date.copyright2018en_US
dc.date.issued2018-07-23
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractIn 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.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/9765
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectOptimal designen_US
dc.subjectStatisticsen_US
dc.subjectSecond-order least squares estimatoren_US
dc.subjectConvex optimizationen_US
dc.subjectGeneralized scale invarianceen_US
dc.subjectNumber of support pointsen_US
dc.titleOptimal regression design under second-order least squares estimator: theory, algorithm and applicationsen_US
dc.typeThesisen_US

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