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1. Hsu, Hsiang-Ling. Optimal designs for statistical inferences in nonlinear models with bivariate response variables.

Degree: PhD, Applied Mathematics, 2011, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0127111-184625

Bivariate or multivariate correlated data may be collected on a sample of unit in many applications. When the experimenters concern about the failure times of two related subjects for example paired organs or two chronic diseases, the bivariate binary data is often acquired. This type of data consists of a observation point x and indicators which represent whether the failure times happened before or after the observation point. In this work, the observed bivariate data can be written with the following form {x, Î´1=I(X1≤ x), Î´2=I(X2≤ x)}.The corresponding optimal design problems for parameter estimation under this type of bivariate data are discussed.
For this kind of the multivariate responses with explanatory variables, their marginal distributions may be from different distributions. Copula model is a way to formulate the relationship of these responses, and the association between pairs of responses. Copula models for bivariate binary data are considered useful in practice due to its flexibility. In this dissertation for bivariate binary data, the marginal functions are assumed from exponential or Weibull distributions and two assumptions, independent or correlated, about the joint function between variables are considered. When the bivariate binary data is assumed correlated, the Clayton copula model is used as the joint cumulative distribution function.
There are few works addressed the optimal design problems for bivariate binary data with copula models. The D-optimal designs aim at minimizing the volume of the confidence ellipsoid for estimating unknown parameters including the association parameter in bivariate copula models. They are used to determine the best observation points. Moreover, the Ds-optimal designs are mainly used for estimation of the important association parameter in Clayton model.
The D- and Ds-optimal designs for the above copula model are found through the general equivalence theorem with numerical algorithm. Under different model assumptions, it is observed that the number of support points for D-optimal designs is at most as the number of model parameters for the numerical results. When the difference between the marginal distributions and the association are significant, the association becomes an influential factor which makes the number of supports gets larger.
The performances of estimation based on optimal designs are reasonably well by simulation studies. In survival experiments, the experimenter customarily takes trials at some specific points such as the position of the 25, 50 and 75 percentile of distributions. Hence, we consider the design efficiencies when the design points for trials are at three or four particular percentiles. Although it is common in practice to take trials at several quantile positions, the allocations of the proportion of sample size also have great influence on the experimental results.
To use a locally optimal design in practice, the prior information for models or parameters are needed. In case there is not enough prior knowledge about the models…
*Advisors/Committee Members: Kam-Fai Wong (chair), Mei-Hui Guo (chair), Ray-Bing Chen (chair), Mong-Na Lo Huang (committee member), Fu-Chuen Chang (chair), Wen-Jang Huang (chair).*

Subjects/Keywords: sequential procedure; simplex dispersion model; rational approximation; optimal design; Bivariate binary data; proportional data; Clayton copula model

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APA (6^{th} Edition):

Hsu, H. (2011). Optimal designs for statistical inferences in nonlinear models with bivariate response variables. (Doctoral Dissertation). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0127111-184625

Chicago Manual of Style (16^{th} Edition):

Hsu, Hsiang-Ling. “Optimal designs for statistical inferences in nonlinear models with bivariate response variables.” 2011. Doctoral Dissertation, NSYSU. Accessed October 20, 2019. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0127111-184625.

MLA Handbook (7^{th} Edition):

Hsu, Hsiang-Ling. “Optimal designs for statistical inferences in nonlinear models with bivariate response variables.” 2011. Web. 20 Oct 2019.

Vancouver:

Hsu H. Optimal designs for statistical inferences in nonlinear models with bivariate response variables. [Internet] [Doctoral dissertation]. NSYSU; 2011. [cited 2019 Oct 20]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0127111-184625.

Council of Science Editors:

Hsu H. Optimal designs for statistical inferences in nonlinear models with bivariate response variables. [Doctoral Dissertation]. NSYSU; 2011. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0127111-184625