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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/89636


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/89636


    Title: 利用最佳A型之集區設計建立最佳A型之行列設計
    Construction of A-optimal row-column designs from the usage of A-optimal block designs
    Authors: 鄭春松
    Contributors: 丁兆平
    鄭春松
    Date: 1991
    1990
    Issue Date: 2016-05-02 17:02:35 (UTC+8)
    Abstract: 實驗設計在工業，醫學，農業上已被廣泛的使用，而尋找最佳之實驗配置也一直是實驗設計重要的課趣。為了測試各處理間之差異，不同評定原則下之最佳設計，在各統計文獻中已多論及。其中含有對照處理之問題又是相當常見，例如:在農業上，我們一直使用某種肥料，若有數種新的肥料被發現，且其可能對於收成有更大的助益，則我們必須做一實驗，分析其結果，然從做一決策以決定新的肥料可否取代原來一直接使用之肥料。而在很多實驗的情形下，實驗者必須利用集區來降低誤差，與增加準確性。所以考慮在集區設計與行列設計之實驗下，如何做實驗配置才可得到最佳設計，正是本文探討的主題。
    我們將考慮在集區設計與行列設計之實驗中ν個實驗處理與一對照處理間之比較，而本文的目的就是要決定一最佳設計，也就是如何配置此ν+ 1個處理，使得在比較實驗處理與對照處理時所得之估計值變異最小，我們將引用Jacroux and Majumdar (1989)中之不等式去證明並得到一些最佳A型集區設計。且利用Jacroux (1986) 之定理與上述之最佳A型集區設計來推廣而證明且得到一些最佳A型行列設計。其中，我們將利用陳武強(1990) 之”猜測”中使用拉丁方格所建立之某些最佳A型行列設計。
    最後，介紹一些我們所得到的最佳A 型設計之建立方式，並舉出一些實例。
    Reference: 1. Bechhofer, R.E. and Tamhane, A.C. (1981). Incomplete block designs for comparing treatments with a control: General Theory. Technometrics, Vol 23, No.1, 45-57.
    2. Cheng, C.S., Majumdar, D., Stufken, J.and Ture, T.E.(1988). Optimal step type designs for comparing test treatments with a control. J.A.S.A. Vol.83, No.402, 477-482.
    3. Hedayat, A.S. and Majumdar, D. (1984). A-optimal incomplete block designs for control-test treatment comparisons.Technometrics. Vol.26, No.4, 363-370.
    4. Hedayat, A.S. and Majumdar, D. (1985). Families of A-optimal block designs for comparing test treatments with a control. Ann. of Stat., vol.13, No.2,757-767.
    5. Jacroux, M. (1986). On the usage of refined linear models for determining N - way classification designs which are optimal for comparing test treatments with a standard treatment. Ann. Inst.Statist.Math.38,569-581.
    6. Jacroux, M. and Majumdar, D (1989). Optimal block designs for comparing test treatments with a control when k >ν. Journal of Statistical Planning and Inference. Vol 23, 381-396.
    7. Kiefer, J. (1958). On the nonrandomized optimality and randomized nonoptimality of symmetrical designs.Ann.Math.Stat. 29, 675-699.
    8. Kiefer, J. (1975). Construction and optimality of generalized Youden designs. ( J. N. Srivastava, ed, ). A survey of statistical design and linear models. North Holland, 333-353.
    9. Majumdar, D. (1986). Optimal design for comparisons between two sets of treatments. Journal of Statistical Planning and Inference. Vol 14, 359-372.
    10. Majumdar, D and Notz, W.I.(1983). Optimal incomplete block designs for comparing treatments with a control. Ann. of stat., Vol.11 , No.1, 258-266.
    11. Notz, W. I. (1985). Optimal designs for treatment-control comparisions in the presence of two-way heterogenity. Journal of Statistical Planning and Inference. Vol 12, 61-73.
    12. Stufken, J. (1987). A-optimal block designs for comparing test treatments with a control. Ann.of stat., Vol. 15, No.4, 1629-1638 .
    13. Ting, C.P. and Notz, W.I.(1989), Optimal row-column designs and block designs for treatment-control comparisions (Submitted for publication).
    14.陳武強.(1990). 含控制處理之雙向分類之最適實驗設計法研究，碩士論文，國立政治大學應用數學研究所。
    Description: 碩士
    國立政治大學
    統計學系
    Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002005022
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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