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研究生:陳乃榮
研究生(外文):Nai-Rong Chen
論文名稱:D最適設計在部分圓上三角迴歸模型
論文名稱(外文):Exact D-optimal designs for linear trigonometric regression models on a partial circle
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:18
中文關鍵詞:線性三角D最適離散設計部分圓近似設計
外文關鍵詞:exact designlinear trigonometricapproximate designD-optimalpartial circle
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在此論文中,我們將要探討有關在部分圓上有截距項跟沒有截距項的
三角迴歸模型離散$D$最適設計的問題,在近代的文章中(Dette,Melas and
Pepelyshev(2001)),已經找到在部分圓上三角迴歸模型的近似$D$最適設計
的精確解。離散最適的設計取決於三角函數的Moment集合的
平均值,而也讓我們知道最適設計的結構其實是跟設計區間的長度和設計
的點數有關的。


In this paper we consider the exact $D$-optimal design problem for
linear trigonometric regression models with or without intercept
on a partial circle. In a recent papper Dette, Melas and
Pepelyshev (2001) found explicit solutions of approximate
$D$-optimal designs for trigonometric regression models with
intercept on a partial circle. The exact optimal designs are
determined by means of moment sets of trigonometric functions. It
is shown that the structure of the optimal designs depends on
both the length of the design interval and the number of the
design points.


Abtract..................................(ii)
Introduction.............................1
Approximate D-optimal designs............2
Exact D-optimal designs..................5
References...............................11
Appendix.................................13


1 Dette, H., Melas, V.B. and Pepelyshev, A. (2001). $D$-optimal designs for trigonometric regression models on a partial circle. Preprint, Ruhr-Universit"at Bochum. http://www.ruhruni-bochum.de/mathematik3/preprint.htm2 Fedorov, V.V. (1972). {it Theory of Optimal Experiments}. Translated and edited by W. J. Studden and E. M. Klimko. Academic press, New York.3 Gaffke, N. (1987). On $D$-optimality of exact linear regression designs with minimum support. {it J. Statist. Plann. Inference} { f 15}, 189-204.4 Hoel, P.G. (1958). Efficiency problems in polynomial estimation. {it Ann. Math. Statist.} { f 29}, 1134-1145.5 Karlin, S. and Studden, W.J.(1966). {it Tchebucheff System: With Applications in Analysis and Statistics}. Wiley, New York.6 Kiefer, J.C. and Wolfowitz, J. (1960). The equivalence of two extremum problems. {it Canad. J. Math.} { f 12}, 363-366.7 Lau, T.S. and Studden, W.J. (1985). Optimal designs for trigonometric and polynomial regression using canonical moments. {it Ann. Statist.} { f 13}, 383-394.8 Pukelsheim, F. (1993). {it optimal Design of Experiments}. Wiley, New York.9 Riccomagno, E., Schwabe, R. and Wynn, H.P. (1997). Lattice-based $D$-optimum design for Fourier regression. {it Ann. Statist.} { f 25}, 2313-2327.10 Wu, H. (1997). Optimal exact designs on a circle or a circular arc. {it Ann. Statist.} { f 25}, 2027-2043.

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