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題名 Φ-最適集區設計之探討
其他題名 .PHI.-Optimal Block Designs for Control-Test Treatment Comparisons.
作者 丁兆平
貢獻者 統計研究所
關鍵詞 區組設計;最佳化設計;A-最適;D-最適
Block design;Optimal design;A-optimality;D-optimality
日期 1996
上傳時間 2-Sep-2014 17:31:45 (UTC+8)
摘要 本計畫旨在探討同時比較v個試驗處理(Test treatment)與一個對照處理(Control treatment)在集區設計(Block design)之架構下,尋找最適設計(Optimal design)之問題。在本計畫中我們導出一個不等式,並利用此一不等式找出.PHI.-最適集區設計之充分條件,由於問題本身之複雜性以及時間之緊迫性,報告中之定理3.10尚有一小部分未臻完善,我們將繼續完成定理3.10之證明。若定理3.10可被完全證出,則許多用以前方法所無法證明其為最適設計之集區設計,其最適性便可證出。
The problem of finding optimal designs for comparing a control simultaneously with v test treatments in the block design setting is studied. A useful inequality for proving optimality is derived. Conditions under which a design is .PHI.-optimal are found under the assumption that Theorem 3.10 is proved completely. These conditions, if the aforementioned theorem is proved completely, generalize previous known results and lead to designs whose optimality cannot be proven using existing methods. We will keep working on the proof of Theorem 3.10, and believe that it can be done in the nearest future.
關聯 行政院國家科學委員會
計畫編號NSC85-2121-M004-002
資料類型 report
dc.contributor 統計研究所en_US
dc.creator (作者) 丁兆平zh_TW
dc.date (日期) 1996en_US
dc.date.accessioned 2-Sep-2014 17:31:45 (UTC+8)-
dc.date.available 2-Sep-2014 17:31:45 (UTC+8)-
dc.date.issued (上傳時間) 2-Sep-2014 17:31:45 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/69612-
dc.description.abstract (摘要) 本計畫旨在探討同時比較v個試驗處理(Test treatment)與一個對照處理(Control treatment)在集區設計(Block design)之架構下,尋找最適設計(Optimal design)之問題。在本計畫中我們導出一個不等式,並利用此一不等式找出.PHI.-最適集區設計之充分條件,由於問題本身之複雜性以及時間之緊迫性,報告中之定理3.10尚有一小部分未臻完善,我們將繼續完成定理3.10之證明。若定理3.10可被完全證出,則許多用以前方法所無法證明其為最適設計之集區設計,其最適性便可證出。en_US
dc.description.abstract (摘要) The problem of finding optimal designs for comparing a control simultaneously with v test treatments in the block design setting is studied. A useful inequality for proving optimality is derived. Conditions under which a design is .PHI.-optimal are found under the assumption that Theorem 3.10 is proved completely. These conditions, if the aforementioned theorem is proved completely, generalize previous known results and lead to designs whose optimality cannot be proven using existing methods. We will keep working on the proof of Theorem 3.10, and believe that it can be done in the nearest future.en_US
dc.format.extent 244 bytes-
dc.format.mimetype text/html-
dc.language.iso en_US-
dc.relation (關聯) 行政院國家科學委員會en_US
dc.relation (關聯) 計畫編號NSC85-2121-M004-002en_US
dc.subject (關鍵詞) 區組設計;最佳化設計;A-最適;D-最適en_US
dc.subject (關鍵詞) Block design;Optimal design;A-optimality;D-optimalityen_US
dc.title (題名) Φ-最適集區設計之探討zh_TW
dc.title.alternative (其他題名) .PHI.-Optimal Block Designs for Control-Test Treatment Comparisons.en_US
dc.type (資料類型) reporten