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題名 A-最適試驗處理與對照處理比較之Diallel Crosses實驗
Families of A-Optimal Diallel Crosses for Test versus Control Comparisons
作者 徐永豐
Hsu, Yung-Feng
貢獻者 丁兆平
Ting, Chao-Ping
徐永豐
Hsu, Yung-Feng
關鍵詞 A-optimality
efficiency
type S block design
type S0 block design
type S design
日期 2003
上傳時間 17-Sep-2009 18:44:05 (UTC+8)
摘要 Diallel cross experiments for comparing p test lines with a control in the set up of block designs and completely randomized designs are investigated. Complete diallel crosses including all p(p+1)/2 distinct crosses are considered. Families of A-optimal and efficient type S0 block designs for p=2,3, and for p>=4, k=2 are obtained, and the construction methods are given. For p>=k>=3, and p>=4, a sufficient condition for type S0 block designs with the control line appearing tb times, where t>=1 is an integer, to be A-optimal is obtained, and families of A-optimal type S0 block designs are provided. The A-optimality of type S designs under the model of completely randomized designs when 2<=p<=6 is also tudied, and some examples are given.
參考文獻 Bechhofer, R.E., Tamhane, A.C. (1981). Incomplete block designs for comparing treatments with a control: General theory, Technometrics 23, 45-57.
Chai, F.S., Mukerjee, R. (1999). Optimal designs for diallel crosses with specific combining abilities, Biometrika 86, 453-458.
Choi, K.C., Gupta, S, Kageyama, S. (2002). Designs for diallel crosses for test versus control comparisons. To appear in Utilitas Math.
Cox, D.R. (1958). Planning of Experiments, Wiley, New York.
Curnow, R. N. (1963). Sampling the diallel cross, Biometrics 19, 287-306.
Das, A. (2002). Efficient Control-Test Designs for diallel cross experiments, isid/ms/2002/12, Indian Statistical Institute, India.
Das, A., Dean, A.M., Gupta, S. (1998). On optimality of some partial diallel cross designs, Sankyuā B 60, 511-524.
Das, A., Dey, A., Dean, A.M. (1998). Optimal designs for diallel cross experiments, Statist. Prob. Letters 36, 427-436.
Das, A., Gupta, S., Kageyama, S. (2002). A-optimal diallel crosses for test versus control comparisons, isid/ms/2002/23, Indian Statistical Institute, India.
Dey, A., Das U.S., Banerjee, A.K. (1986). Construction of nested balanced incomplete block designs, Calcutta Statist. Assoc.Bull. 35, 161-167.
Dey, A., Midha, C.K. (1996). Optimal block designs for diallel crosses, Biometrika 83, 484-489.
Finney, D. J. (1958b). Plant selection for yield improvement, Euphytica 7, 83-106.
Gilbert, N. E. G. (1958). Diallel cross in plant breeding, Heredity 12, 477-492.
Griffing, B. (1956). Concept of general and specific combining ability in relation to diallel crossing systems, Aust. J. Biol. Sci. 9, 463-493.
Gupta, S. (1989). Efficient designs for comparing test treatments with a control treatment, Biometrika 76, 783-787.
Gupta, S., Das, A., Kageyama, S. (1995). Single replicate orthogonal block designs for circulant partial diallel crosses, Commun. Statist. 24, 2601-2607.
Gupta, S., Kageyama, S. (1994). Optimal complete diallel crosses, Biometrika 81, 420-424.
Hedayat, A.S., Majumdar, D. (1984). A-optimal incomplete block designs for control-test treatment comparisons, Technometrics 26, 363-370.
Hedayat, A.S., Majumdar, D. (1985). Families of A-optimal block designs for comparing test treatments with a control, Ann. Statist. 13, 757-767.
Hinkelmann, K. (1975). Design of genetic experiments, In: J.N. Srivastava (Ed.), A Survey of Statistical Design and Linear Models, North-Holland, Amsterdam, pp. 243-269.
Jacroux, M., Majumdar, D. (1989). Optimal block designs for comparing test treatments with a control when k > v, J. Statist. Plan. Infer. 23, 381-396.
Kiefer, J. (1975). Constructions and optimality of generalized Youden Designs, In: J.N. Srivastava (Ed.), A Survey of Statistical Design and Linear Models, North-Holland, Amsterdam, pp. 333-353.
Majumdar, D. (1996). Optimal and efficient treatment-control designs, In: S. Ghosh, C. R. Rao (Ed.), Handbook of Statistics 13, North-Holland, Amsterdam, pp. 1007-1053.
Majumdar, D., Notz, W. (1983). Optimal incomplete block designs for comparing treatments with a control, Ann. Statist. 11, 258-266.
Morgan, J.P., Preece, D.A., Rees, D.H. (2001). Nested balanced incomplete block designs, Discrete Mathematics 231, 351-389.
Mukerjee, R. (1997). Optimal partial diallel crosses, Biometrika 84, 939-948.
Preece D. A. (1967). Nested balanced incomplete block designs, Biometrika 54, 479-486.
Singh, M., Hinkelmann, K. (1990). On generation of efficient partial diallel crosses plans, Biom. J. 32, 177-187.
Yates, F. (1950). Recent applications of biometrical methods in genetics, Biometrics 6, 200-207.
描述 博士
國立政治大學
統計研究所
86354504
92
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0086354504
資料類型 thesis
dc.contributor.advisor 丁兆平zh_TW
dc.contributor.advisor Ting, Chao-Pingen_US
dc.contributor.author (Authors) 徐永豐zh_TW
dc.contributor.author (Authors) Hsu, Yung-Fengen_US
dc.creator (作者) 徐永豐zh_TW
dc.creator (作者) Hsu, Yung-Fengen_US
dc.date (日期) 2003en_US
dc.date.accessioned 17-Sep-2009 18:44:05 (UTC+8)-
dc.date.available 17-Sep-2009 18:44:05 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 18:44:05 (UTC+8)-
dc.identifier (Other Identifiers) G0086354504en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/33888-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 86354504zh_TW
dc.description (描述) 92zh_TW
dc.description.abstract (摘要) Diallel cross experiments for comparing p test lines with a control in the set up of block designs and completely randomized designs are investigated. Complete diallel crosses including all p(p+1)/2 distinct crosses are considered. Families of A-optimal and efficient type S0 block designs for p=2,3, and for p>=4, k=2 are obtained, and the construction methods are given. For p>=k>=3, and p>=4, a sufficient condition for type S0 block designs with the control line appearing tb times, where t>=1 is an integer, to be A-optimal is obtained, and families of A-optimal type S0 block designs are provided. The A-optimality of type S designs under the model of completely randomized designs when 2<=p<=6 is also tudied, and some examples are given.zh_TW
dc.description.tableofcontents 1. Introduction 1
2. Preliminaries 5
3. Optimal and Efficient Designs for p=2,3, and for p>=4,
k=2 11
3.1. Optimal and Efficient Designs for p=3 11
3.2. Efficient Designs for p=2 18
3.3. Optimal and Efficient Designs for p>=4, k=2 25
4. A-Optimal Designs for p>=k 32
4.1. A-Optimal Designs for [(2bk-sd0)/pb]=0 32
4.1.1. A-Optimal Designs for t=1 43
4.1.2. A-Optimal Designs for t>=2 48
4.2. A-Optimal Designs for [(2bk-sd0)/pb]=1 57
5. A-Optimality of Completely randomized Designs 82
5.1. Optimal Designs for p=2,3 82
5.2. Optimal Designs for 4<=p<=6 89		zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0086354504en_US
dc.subject (關鍵詞) A-optimalityen_US
dc.subject (關鍵詞) efficiencyen_US
dc.subject (關鍵詞) type S block designen_US
dc.subject (關鍵詞) type S0 block designen_US
dc.subject (關鍵詞) type S designen_US
dc.title (題名) A-最適試驗處理與對照處理比較之Diallel Crosses實驗zh_TW
dc.title (題名) Families of A-Optimal Diallel Crosses for Test versus Control Comparisonsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Bechhofer, R.E., Tamhane, A.C. (1981). Incomplete block designs for comparing treatments with a control: General theory, Technometrics 23, 45-57.zh_TW
dc.relation.reference (參考文獻) Chai, F.S., Mukerjee, R. (1999). Optimal designs for diallel crosses with specific combining abilities, Biometrika 86, 453-458.zh_TW
dc.relation.reference (參考文獻) Choi, K.C., Gupta, S, Kageyama, S. (2002). Designs for diallel crosses for test versus control comparisons. To appear in Utilitas Math.zh_TW
dc.relation.reference (參考文獻) Cox, D.R. (1958). Planning of Experiments, Wiley, New York.zh_TW
dc.relation.reference (參考文獻) Curnow, R. N. (1963). Sampling the diallel cross, Biometrics 19, 287-306.zh_TW
dc.relation.reference (參考文獻) Das, A. (2002). Efficient Control-Test Designs for diallel cross experiments, isid/ms/2002/12, Indian Statistical Institute, India.zh_TW
dc.relation.reference (參考文獻) Das, A., Dean, A.M., Gupta, S. (1998). On optimality of some partial diallel cross designs, Sankyuā B 60, 511-524.zh_TW
dc.relation.reference (參考文獻) Das, A., Dey, A., Dean, A.M. (1998). Optimal designs for diallel cross experiments, Statist. Prob. Letters 36, 427-436.zh_TW
dc.relation.reference (參考文獻) Das, A., Gupta, S., Kageyama, S. (2002). A-optimal diallel crosses for test versus control comparisons, isid/ms/2002/23, Indian Statistical Institute, India.zh_TW
dc.relation.reference (參考文獻) Dey, A., Das U.S., Banerjee, A.K. (1986). Construction of nested balanced incomplete block designs, Calcutta Statist. Assoc.Bull. 35, 161-167.zh_TW
dc.relation.reference (參考文獻) Dey, A., Midha, C.K. (1996). Optimal block designs for diallel crosses, Biometrika 83, 484-489.zh_TW
dc.relation.reference (參考文獻) Finney, D. J. (1958b). Plant selection for yield improvement, Euphytica 7, 83-106.zh_TW
dc.relation.reference (參考文獻) Gilbert, N. E. G. (1958). Diallel cross in plant breeding, Heredity 12, 477-492.zh_TW
dc.relation.reference (參考文獻) Griffing, B. (1956). Concept of general and specific combining ability in relation to diallel crossing systems, Aust. J. Biol. Sci. 9, 463-493.zh_TW
dc.relation.reference (參考文獻) Gupta, S. (1989). Efficient designs for comparing test treatments with a control treatment, Biometrika 76, 783-787.zh_TW
dc.relation.reference (參考文獻) Gupta, S., Das, A., Kageyama, S. (1995). Single replicate orthogonal block designs for circulant partial diallel crosses, Commun. Statist. 24, 2601-2607.zh_TW
dc.relation.reference (參考文獻) Gupta, S., Kageyama, S. (1994). Optimal complete diallel crosses, Biometrika 81, 420-424.zh_TW
dc.relation.reference (參考文獻) Hedayat, A.S., Majumdar, D. (1984). A-optimal incomplete block designs for control-test treatment comparisons, Technometrics 26, 363-370.zh_TW
dc.relation.reference (參考文獻) Hedayat, A.S., Majumdar, D. (1985). Families of A-optimal block designs for comparing test treatments with a control, Ann. Statist. 13, 757-767.zh_TW
dc.relation.reference (參考文獻) Hinkelmann, K. (1975). Design of genetic experiments, In: J.N. Srivastava (Ed.), A Survey of Statistical Design and Linear Models, North-Holland, Amsterdam, pp. 243-269.zh_TW
dc.relation.reference (參考文獻) Jacroux, M., Majumdar, D. (1989). Optimal block designs for comparing test treatments with a control when k > v, J. Statist. Plan. Infer. 23, 381-396.zh_TW
dc.relation.reference (參考文獻) Kiefer, J. (1975). Constructions and optimality of generalized Youden Designs, In: J.N. Srivastava (Ed.), A Survey of Statistical Design and Linear Models, North-Holland, Amsterdam, pp. 333-353.zh_TW
dc.relation.reference (參考文獻) Majumdar, D. (1996). Optimal and efficient treatment-control designs, In: S. Ghosh, C. R. Rao (Ed.), Handbook of Statistics 13, North-Holland, Amsterdam, pp. 1007-1053.zh_TW
dc.relation.reference (參考文獻) Majumdar, D., Notz, W. (1983). Optimal incomplete block designs for comparing treatments with a control, Ann. Statist. 11, 258-266.zh_TW
dc.relation.reference (參考文獻) Morgan, J.P., Preece, D.A., Rees, D.H. (2001). Nested balanced incomplete block designs, Discrete Mathematics 231, 351-389.zh_TW
dc.relation.reference (參考文獻) Mukerjee, R. (1997). Optimal partial diallel crosses, Biometrika 84, 939-948.zh_TW
dc.relation.reference (參考文獻) Preece D. A. (1967). Nested balanced incomplete block designs, Biometrika 54, 479-486.zh_TW
dc.relation.reference (參考文獻) Singh, M., Hinkelmann, K. (1990). On generation of efficient partial diallel crosses plans, Biom. J. 32, 177-187.zh_TW
dc.relation.reference (參考文獻) Yates, F. (1950). Recent applications of biometrical methods in genetics, Biometrics 6, 200-207.zh_TW