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研究生:廖漢忠
研究生(外文):Hao-Chung Liao
論文名稱:交換式演算法建構連續最適設計
論文名稱(外文):Construction of approximate optimal designs by exchange algorithm
指導教授:張福春張福春引用關係
指導教授(外文):Fu-Chuen Chang
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:21
中文關鍵詞:連續最適設計離散最適設計A-最優交換式演算法D-最優
外文關鍵詞:D-optimaapproximateexactexchange algorithm
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本研究將考慮利用交換式演算法,計算一個變數線性迴歸模型之數值最適設計解的可行性。而關於最適設計必須有最少支撐點的充分條件在Fedorov(1972)中的定理2.3.2 中眾所皆知。然而,只有一些情況之下,分析這最適設計是眾所皆知的,即針對多數判別式我們較容易採用計算最適設計的交換程序。因此,我們為建構著名的特別情況來描述在這利用D型、A型和有支撐點最少的c型等最適的設計,並舉出如何能夠用這個演算法來獲得這些最適設計的例子並且討論演算法的表現好壞,並利用一般使用的最適設計標準:D,A,c 標準來為產生一系列迴歸函數而形成一個柴比雪夫系統的迴歸模型來研究演算法的收斂性優劣。
In this study we will consider the construction of approximate optimal design for one-dimensional regression by exchange algorithm. Sufficient conditions under which an optimal design must have the minimal support points are known in Theorem 2.3.2 of Fedorov (1972). However, there are only a few cases which the analytic optimal designs are known. The exchange procedure for
computing optimal designs is easily adopted to most criteria. We describe implementations for constructing the well-known special cases D-, A-, and c-optimal designs with the minimum number of
support points. Examples which illustrate how the algorithm can be used to obtain these optimal designs and the performance of the algorithm are discussed. The commonly used D-, A-, and c-optimal
criteria will be employed to study the convergence properties of the exchange algorithm for regression model which the set of the product of regression functions forms a Chebyshev system.
Abstract..............................1
Introduction..........................3
Preliminary...........................4
Algorithms............................7
tem Examples and simulation results...10
Conclusiondotfill....................13
Reference
Reference
Cook, R. D. and Nachtsheim, C. J. (1980). A comparison of algorithm
for constructing exact D-optimal designs, Technometrics, 22, 315-324.
Fedorov, V. V. (1972). Theory of Optimal Experiments. Translated and
edited by W. J. Studden and E. M. Klimko. Academic press, New
York.
Nguyen, N. K. and Miller, A. J. (1992). A review of some exchange
algorithms for constructing discrete D-optimal designs. Computat.
Statist. Data Anal., 14, 489-498.
Miller, A. J. and Nguyen, N. K. (1994). A Fedorov exchange algorithm for D- optimal design. Applied. Stat., 43, 669-677.
Pukelsheim, F. (1993). Optimal Design of Experiments. Wiley, New York.
Wald, A. (1943). On the efficient design of statistical
investigations. Ann. Math. Stat., 14, 134-140.
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