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題名 對照處理與4或6個試驗處理比較之最佳群可分集區設計之研究 作者 張萃貞 貢獻者 朗冰瑩
張萃貞日期 1991
1990上傳時間 2-五月-2016 17:02:51 (UTC+8) 摘要 含對照處理之區集實驗設計是將對照處理及v個試驗處理配置在b 個大小為k 的區集中實驗.本文針對k=3,v =4 或6之群可分集區設計(Group-Divisible Treatment Design) 探討:給定λ0 ， λ1 ，λ2 後，對具有最少區集數目b 之設計，何者可達到A-Optimal，若無法達到A-Optimal 又以何者較有效率. 由結果中可知:具有最少區集數目之A-Optimal GDTD，其λ0 γ0 有特定之關係。 參考文獻 [1] Bechhofer, R. E., and Tamhane, A. C. (1981), Incomplete block designs for comparing treatments with a control. Technometrics , 23 , 45-57. [2] Cheng , C. S. (1978) , Optimality of certain asymmetrical designs. The Annals of Statistics , 6 , 1239-1261. [3] Hedayat, A. S., and Majumdar, D.(1984), A-optimal black designs for control-test treatment comparisions. Technometrics, 26,363-370. [4] Hedayat , A. S., and Majumdar, D.(1985), A-optimal black designs for comparing test treatments with a control. The Annals of Statistics,6, 757-767. [5] Jacroux, M. (1985) , Some sufficient conditions for the type 1 optimality of block designs. Journal of Statistical Planning and Inference , 11. 385-398. [6] Jacroux, M. (1987a). On the determination and construction of MV - optimal block designs for comparing test treatments with a standard treatment. Journal of Statistical Planning and Inference. 15 , 205-225. [7] Jacroux, M.(1987b). On the A-optimality of block designs for comparing test treatmcnts with a control. technical report , Washington State University.Dept. of Hathematical Sciences. [8] Jacroux, M.(1989), On the A-optimality of block designs for comparing test treatments with a control. J. Amer. Statist. Assoc. 84, 310-317. [9] Kiefer, J. (1975), Construction and optimality of generalized Youden designs. A Survey of Statistical Design and I.inear Models(J.Srivastava ed.), North Holland, New Yark,333-353. [10] Majumdar , D., and Notz, W. (1983), Optimal incomplete block designs for comparing treatments with a control. The Annals of Statistics, 11. 258-266. [11] Notz. W. and Tamhane. A. C. (1983) , Balanced treatment incomplete block designs for comparing treatments with a control: Minimal complete sets for generator designs for k = 3, p = 3(1) 10. Comm. Statist. A - Theory Methods 12. 1391-1412. [12]Stufken, J.(1987), A-Optimal block designs for comparing test treatments with a control. The Annals of Statistics, 15, 1629-1638. [13] Stufke. J. (1987) , On group divisible treatment designs for comparing test treatments with a standard treatment in blocks of size 3. International statistical symposium Taipei , R.O.C 描述 碩士
國立政治大學
統計學系資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002005030 資料類型 thesis dc.contributor.advisor 朗冰瑩 zh_TW dc.contributor.author (作者) 張萃貞 zh_TW dc.creator (作者) 張萃貞 zh_TW dc.date (日期) 1991 en_US dc.date (日期) 1990 en_US dc.date.accessioned 2-五月-2016 17:02:51 (UTC+8) - dc.date.available 2-五月-2016 17:02:51 (UTC+8) - dc.date.issued (上傳時間) 2-五月-2016 17:02:51 (UTC+8) - dc.identifier (其他 識別碼) B2002005030 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/89643 - 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.abstract (摘要) 含對照處理之區集實驗設計是將對照處理及v個試驗處理配置在b 個大小為k 的區集中實驗.本文針對k=3,v =4 或6之群可分集區設計(Group-Divisible Treatment Design) 探討:給定λ0 ， λ1 ，λ2 後，對具有最少區集數目b 之設計，何者可達到A-Optimal，若無法達到A-Optimal 又以何者較有效率. 由結果中可知:具有最少區集數目之A-Optimal GDTD，其λ0 γ0 有特定之關係。 zh_TW dc.description.tableofcontents 第一章 簡介.................................1 第一節 引言.................................1 第二節 模型.................................3 第三節 最適A型設計.................................5 第四節 群可分集區設計(GDTD) .................................6 第二章 文獻回顧.................................7 第一節 最適A型設計之充分條件.................................7 第二節 v=4 或 6，k=3 之特定參數下最少區集之設計.................................11 第三章 最適A型 GDTD之研究.................................20 第一節 最適A型設計之搜尋.................................20 第二節 討論.................................22 第四章 討論.................................26 第五章 其他具高效率之GDTD.................................29 附錄A ....................................... 33 附錄B.................................35 附錄C .................................36 附錄D.................................38 附錄E.................................39 參考文獻.................................40 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002005030 en_US dc.title (題名) 對照處理與4或6個試驗處理比較之最佳群可分集區設計之研究 zh_TW dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Bechhofer, R. E., and Tamhane, A. C. (1981), Incomplete block designs for comparing treatments with a control. Technometrics , 23 , 45-57. [2] Cheng , C. S. (1978) , Optimality of certain asymmetrical designs. The Annals of Statistics , 6 , 1239-1261. [3] Hedayat, A. S., and Majumdar, D.(1984), A-optimal black designs for control-test treatment comparisions. Technometrics, 26,363-370. [4] Hedayat , A. S., and Majumdar, D.(1985), A-optimal black designs for comparing test treatments with a control. The Annals of Statistics,6, 757-767. [5] Jacroux, M. (1985) , Some sufficient conditions for the type 1 optimality of block designs. Journal of Statistical Planning and Inference , 11. 385-398. [6] Jacroux, M. (1987a). On the determination and construction of MV - optimal block designs for comparing test treatments with a standard treatment. Journal of Statistical Planning and Inference. 15 , 205-225. [7] Jacroux, M.(1987b). On the A-optimality of block designs for comparing test treatmcnts with a control. technical report , Washington State University.Dept. of Hathematical Sciences. [8] Jacroux, M.(1989), On the A-optimality of block designs for comparing test treatments with a control. J. Amer. Statist. Assoc. 84, 310-317. [9] Kiefer, J. (1975), Construction and optimality of generalized Youden designs. A Survey of Statistical Design and I.inear Models(J.Srivastava ed.), North Holland, New Yark,333-353. [10] Majumdar , D., and Notz, W. (1983), Optimal incomplete block designs for comparing treatments with a control. The Annals of Statistics, 11. 258-266. [11] Notz. W. and Tamhane. A. C. (1983) , Balanced treatment incomplete block designs for comparing treatments with a control: Minimal complete sets for generator designs for k = 3, p = 3(1) 10. Comm. Statist. A - Theory Methods 12. 1391-1412. [12]Stufken, J.(1987), A-Optimal block designs for comparing test treatments with a control. The Annals of Statistics, 15, 1629-1638. [13] Stufke. J. (1987) , On group divisible treatment designs for comparing test treatments with a standard treatment in blocks of size 3. International statistical symposium Taipei , R.O.C zh_TW
