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研究生:丁大宇
研究生(外文):Da-Yu Ting
論文名稱:二項分配之序貫估計
論文名稱(外文):Estimations Following Sequential Comparison of Two Binomial Populaions
指導教授:翁久幸
指導教授(外文):Chiu-Hsing Weng
學位類別:碩士
校院名稱:國立政治大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2000
畢業學年度:88
語文別:英文
論文頁數:27
外文關鍵詞:binary dataconfidence setssequential estimationssigned-root transformation
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Consider sequential trials comparing two treatments with binary responses. The goal is to derive accurate confidence sets for the treatment difference and the individual success probabilities of the two treatments. We shall begin with the signed-root transformation as a pivot and then apply the approximate theory of Weng and Woodroofe [11] to form accurate confidence sets of these parameters. The explicit correction terms of the pivots are obtained. The simulation studies agree well with the theoretical results.
List of Figures
List of Tables
1. Introduction 1
2. The Model 3
2.1 The Log-Odds-Ratio θ1 3
2.2 The Individual Success Probabilities pi 6
3. Accurate Confidence Sets 9
3.1 Confidence Sets for Log-Odds-Ratio θ1 9
3.2 Confidence Sets for pi 13
4. Discussions 17
5. References 18
6. Appendix 20
[1] P. Armitage. Numerical studies in the sequential estimation of a binomial parameter. Biometrika, 45:1-15, 1958.
[2] I.V. Basawa and B. L. S. P. Rao, Stochastic Process. Academic Press, London, 1980.
[3] M. N. Chang. Confidence intervals for a normal mean following a group sequential test. Biometrics, 45:247-254, 1989.
[4] D. S. Coad and M. Woodroofe. Corrected confidence intervals after sequential testing with applications to survival analysis. Biometrika, 83:763-777, 1996.
[5] K. M. Facey and J. Whitehead. An improved approximation for calculation of confidence intervals after a sequential clinical trial. Statist. Med., 9:1277-1285, 1990.
[6] G. L. Rosner and A. A. Tsiatis. Exact confidence limits following group sequential test. Biometrika, 75:723-729, 1988.
[7] D. Siegmund. Estimation following sequential testing. Biometrika, 65:341-349, 1978.
[8] D. Siemund. Sequential Analysis. Springer, New York, 1985.
[9] S. Todd and J. Whitehead. Confidence interval calculation for a sequential clinical trial of binary responses. Biometrika, 84:737-743, 1997.
[10] S. Todd, J. Whitehead, and K. M. Facey. Point and interval estimation following a sequential clinical trial. Biometrika, 83:453-461, 1996.
[11] R. C. Weng and M. Woodroofe. Integrable expansions for posterior distributions for multiparameter exponential families with applications to sequential confidence levels. Statistica Sinica, 10:693-713, 2000.
[12] J. Whitehead. The Design and Analysis of Sequential Clinical Trials. Ellis Horwood, Chichester, 1983.
[13] M. Woodroofe. Very weak expansions for sequentially designed experiments: linear models. Ann. Statist., 17:1087-1102, 1989.
[14] M. Woodroofe. Estimation after sequential testing : A simple approach for a truncated sequential probability ratio test. Biometrika, 79:347-353, 1992.
[15] M. Woodroofe. Integrable expansions for posterior distributions for one-parameter exponential families. Statistica Sinica, 2:91-111, 1992.
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