學術產出-Theses
Article View/Open
Publication Export
-
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-Mar-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-Hsing en_US dc.contributor.author (Authors) 丁大宇 zh_TW dc.contributor.author (Authors) Ting, Da-Yu en_US dc.creator (作者) 丁大宇 zh_TW dc.creator (作者) Ting, Da-Yu en_US dc.date (日期) 2000 en_US dc.date.accessioned 31-Mar-2016 14:44:58 (UTC+8) - dc.date.available 31-Mar-2016 14:44:58 (UTC+8) - dc.date.issued (上傳時間) 31-Mar-2016 14:44:58 (UTC+8) - dc.identifier (Other Identifiers) A2002001946 en_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) 87354005 zh_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. Introduction2. The Model2.1 The Log-Odds-Ratio θ12.2 The Individual Success Probabilities pi3. Accurate Confidence Sets3.1 Confidence Sets for Log-Odds-Ratio θ13.2 Confidence Sets for pi4. Discussions5. References6. Appendix zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001946 en_US dc.subject (關鍵詞) binary data en_US dc.subject (關鍵詞) confidence sets en_US dc.subject (關鍵詞) sequential estimations en_US dc.subject (關鍵詞) signed-root transformation en_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 Populations en_US dc.type (資料類型) thesis en_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
