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論文名稱 Title |
二元反應模型之模型區分及模型穩健最適設計 Optimum Designs for Model Discrimination and Estimation in Binary Response Models |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
36 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2005-06-03 |
繳交日期 Date of Submission |
2005-06-29 |
關鍵字 Keywords |
模型穩健、模型區分、對稱之位置與尺度族、最小平方估計量、均方差 Least square estimate, model robustness, model discrimination, mean square error, symmetric location and scale family |
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統計 Statistics |
本論文已被瀏覽 5721 次,被下載 1434 次 The thesis/dissertation has been browsed 5721 times, has been downloaded 1434 times. |
中文摘要 |
此篇論文所討論的問題是關於尋找一最適設計,其具有模型區分的作用,並同時具有模型穩健的性質。在此篇論文當中,模型穩健的想法是在於假設之模型與真實之模型間,最大的模型偏差可以被最小化。其中,關於模型區分部分的標準是基於 Atkinson 與 Fedorov (1975) 所提出的T-最適設計標準,滿足此一標準的設計能使得在於設計點上的模型誤差平方和達到最大。另外,關於模型穩健設計部分的標準,採用的則是使得兩競爭的模型間,最大的差距最小化的標準。在此篇文章中,我們對於一些常用的二元反應模型,例如 Probit 或者是 Logit模型等,找出了滿足上述兩個標準的最適設計。 |
Abstract |
This paper is concerned with the problem of finding an experimental design for discrimination between two rival models and for model robustness that minimizing the maximum bias simultaneously in binary response experiments. The criterion for model discrimination is based on the $T$-optimality criterion proposed in Atkinson and Fedorov (1975), which maximizes the sum of squares of deviations between the two rival models while the criterion for model robustness is based on minimizing the maximum probability bias of the two rival models. In this paper we obtain the optimum designs satisfy the above two criteria for some commonly used rival models in binary response experiments such as the probit and logit models etc. |
目次 Table of Contents |
Introduction Desired TLS-optimum design Efficiency and bias comparisons Discussions and conclusions |
參考文獻 References |
Atkinson, A. C., and Fedorov, V. V. (1975). Optimal design: Experiments for discriminating between several models. Biometrika, 62, 289-304. Chambers, E. A. and Cox, D.R. (1967). Discrimination between alternative binary response models. Biometrika, 54, No.3/4, 573-578. Dette, H., and Sahm, M. (1997). Standardized optimal designs for binary response experiments. South African Statistical Journal, 31, 271-298. Huang, M-N. L. and Hwang, S-H. (2004). Model robust designs for binary response experiments. Department of Applied Mathematics, National Sun Yat-sen University, Manuscript. Minkin, S. (1987). Optimal designs for binary data. Journal of the American Statistical Association, 82, 1098-1103. Muller, W. G., and Ponce de Leon, A. C. M. (1996). Discrimination between two binary data models: Sequentially designed experiments. Journal of Statistical Computation and Simulation, 55 , 87-100. Sitter, R. R., and Wu, C. F. J. (1993). Optimal designs for binary response experiments: Fieller, D-, and A- criteria. Scandinavian Journal of Statistics, 20, 329-341. Sitter, R. R., and Fainaru, I. (1997). Optimal designs for the logit and probit models for binary data. The Canadian Journal of Statistics, 25, 175-190. Ucinski, D. and Bogacka, B. (2004). T-optimum designs for discrimination between two multiresponse dynamic models. Journal of the Royal Statistical Society Series B}, 67, No.1, 3-18. Wu, C. F. J. (1985). Efficient sequential designs with binary data. Journal of the American Statistical Association, 80, 974-984. Wu, C. F. J. (1988). Optimal design for percentile estimation of a quantal response curve. Optimal Design and Analysis of Experiments, 213-224. Yanagisawa, Y. (1988). Designs for discrimination between binary response models. Journal of Statistical Planning and Inference, 19 , 31-41. Yanagisawa, Y. (1990). Designs for discrimination between bivariate binary response models. Biometrical Journal, 32, 25-34. |
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