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論文名稱 Title |
D最適設計在部分圓上三角迴歸模型
Exact D-optimal designs for linear trigonometric regression models on a partial circle |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
18 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2002-05-31 |
繳交日期 Date of Submission |
2002-07-22 |
關鍵字 Keywords |
線性三角、D最適、離散設計、部分圓、近似設計 exact design, linear trigonometric, approximate design, D-optimal, partial circle |
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統計 Statistics |
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中文摘要 |
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。 |
Abstract |
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. |
目次 Table of Contents |
Abtract..................................(ii) Introduction.............................1 Approximate D-optimal designs............2 Exact D-optimal designs..................5 References...............................11 Appendix.................................13 |
參考文獻 References |
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.htm 2 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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