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研究生:葉家明
研究生(外文):Chia-Min Yeh
論文名稱:雙變量存活資料的參數檢定之C-最適設計
論文名稱(外文):C-optimal Designs for Parameter Testing with Survival Data under Bivariate Copula Models
指導教授:羅夢娜羅夢娜引用關係
指導教授(外文):Mong-Na Lo Huang
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:英文
論文頁數:37
中文關鍵詞:檢測時間二階段估計概似比檢定Pearson 卡方檢定c-最適設計
外文關鍵詞:two-stage estimationlikelihood ratio testPearson chi-square testinspection timecurrent status datac-optimal design
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在許多領域的問題中,經常會遇到與現狀數據有關的情形。針對一個不易觀察的實際失效時間,而只知道此時間是高於或低於一個隨機的檢測時間。在此篇論文中,我們考慮的是雙變量現狀數據,並且假設我們對此雙變量的失效時間有些先驗訊息。我們最主要的目標,是找到一個最適的檢測時間,來檢定兩者之間的關係。
Current status data are usually obtained with a failure time variable T which is diffcult observed but can be determined to lie below or above a random monitoring time or inspection time t. In this work we consider bivariate current status data ${t,delta_1,delta_2}$ and assume we have some prior information of the bivariate failure time variables T1 and T2. Our main goal is to find an optimal inspection time for testing the relationship between T1 and T2.
Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Optimal design criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Inferences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3. Optimal design for testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1 Under independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Under association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4. Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.1 Test of association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2 Test under independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.3 Estimate of parameters and association . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.4 Test under association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5. Conclusion and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
References
1. Agresti, A. (2002). Categorical Data Analysis. New York: Wiley.
2. Atkinson, A. C. and Donev, A. N. (1991). Optimum Experimental Designs.
Oxford: Clarendon Press.
3. Casella, G. and Berger, R. L. (2002). Statistical Inference. Paci‾c Grove, CA:
Duxbury Press.
4. Clayton, D. G. (1978). A model for association in bivariate life tables and its
application in epidemiological studies of familial tendency in chronic disease
incidence. Biometrika 65, 141-151.
5. Cox, D. R. and Hinkley, D. V. (1974). Theoretical Statistics. London: Chap-
man and Hall.
6. Fedorov, V. V. and Studden, W. J. and Klimko, E. M. (1972). Theory of
Optimal Experiments. New York and London: Academic Press.
7. Fujii, Y. (1990). Models for association in bivariate survival data. Environ-
mental Health Perspectives 87, 131-134.
8. Genest, C. and MacKay, R. J. (1986). The joy of copulas: bivariate distribu-
tions with uniform marginals. Annals of Statistics 40, 280-283.
9. Genest, C. and Rivest, L. P. (1993). Statistical inference procedures for bi-
variate Archimedean copulas. Journal of the American Statistical Association
88, 1034-1043.
10. Hougaard, P. (1986). A class of multivariate failure time distributions. Biometrika
73, 671-678.
11. Lin, D. Y. and Oakes, D. and Ying, Z. (1998). Additive hazards regression
with current status data. Biometrika 85, 289-298.
12. Meeker, W. Q. and Escobar, L. A. (1998). Statistical Methods for Reliability
Data. New York: Wiley.
13. Oakes, D. (1982). A model for association in bivariate survival data. Journal
of the Royal Statistical Society. Series B 44, 414-422.
14. Shih, J. H. and Louis, T. A. (1995). Inferences on the association parameter
in copula models for bivariate survival data. Biometrics 51, 1384-1399.
19
15. Shih, J. H. and Louis, T. A. (1996). Tests of independence for bivariate survival
data. Biometrics 52, 1440-1449.
16. Wang, W. and Ding, A. A. (2000). On assessing the association for bivariate
current status data. Biometrika 87, 879-893.
17. Wang, W. and Wells, M. T. (2000). Model selection and semiparametric
inference for bivariate failure-time data. Journal of the American Statistical
Association 95, 62-72.
18. White, L. V. (1973). An extension of the general equivalence theorem to
nonlinear models. Biometrika 60, 345-348.
19. Wilks, S. S. (1935). On the independent of k sets of normally distributed
statistical variables. Econometrica 3, 309-326.
20. Wilks, S. S. (1938). The large-sample distribution of the likelihood ratio for
testing composite hypotheses. Annals of Mathematical Statistics 9, 60-62.
21. Yates, F. (1934). Contingency table involving small numbers and the $chi^2$ test.
Journal of the Royal Statistical Society (Supplement) 1: 217-235.
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