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題名 二項分配之序貫估計
Estimations Following Sequential Comparison of Two Binomial Populations
作者 丁大宇
Ting, Da-Yu
貢獻者 翁久幸
Weng, Chiu-Hsing
丁大宇
Ting, Da-Yu
關鍵詞 binary data
confidence sets
sequential estimations
signed-root transformation
日期 2000
上傳時間 31-三月-2016 14:44:58 (UTC+8)
摘要 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.
參考文獻 [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.
描述 碩士
國立政治大學
統計學系
87354005
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001946
資料類型 thesis
dc.contributor.advisor 翁久幸zh_TW
dc.contributor.advisor Weng, Chiu-Hsingen_US
dc.contributor.author (作者) 丁大宇zh_TW
dc.contributor.author (作者) Ting, Da-Yuen_US
dc.creator (作者) 丁大宇zh_TW
dc.creator (作者) Ting, Da-Yuen_US
dc.date (日期) 2000en_US
dc.date.accessioned 31-三月-2016 14:44:58 (UTC+8)-
dc.date.available 31-三月-2016 14:44:58 (UTC+8)-
dc.date.issued (上傳時間) 31-三月-2016 14:44:58 (UTC+8)-
dc.identifier (其他 識別碼) A2002001946en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/83252-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 87354005zh_TW
dc.description.abstract (摘要) 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.en_US
dc.description.tableofcontents 封面頁
證明書
致謝詞
論文摘要
目錄
圖目錄
表目錄
1. Introduction
2. The Model
2.1 The Log-Odds-Ratio θ1
2.2 The Individual Success Probabilities pi
3. Accurate Confidence Sets
3.1 Confidence Sets for Log-Odds-Ratio θ1
3.2 Confidence Sets for pi
4. Discussions
5. References
6. Appendix		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001946en_US
dc.subject (關鍵詞) binary dataen_US
dc.subject (關鍵詞) confidence setsen_US
dc.subject (關鍵詞) sequential estimationsen_US
dc.subject (關鍵詞) signed-root transformationen_US
dc.title (題名) 二項分配之序貫估計zh_TW
dc.title (題名) Estimations Following Sequential Comparison of Two Binomial Populationsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [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.		zh_TW