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博碩士論文 etd-0625107-112338 詳細資訊
Title page for etd-0625107-112338
論文名稱
Title
多項式迴歸模型具權重函數 exp(alpha x)之D 最適設計
D-optimal designs for polynomial regression with weight function exp(alpha x)
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
20
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2007-05-24
繳交日期
Date of Submission
2007-06-25
關鍵字
Keywords
Legendre 多項式、D 最適設計、Laguerre 多項式、arcsin 分布、D 等價定理、夾擠定理
Squeeze Theorem, Legendre polynomial, Laguerre polynomial, D-Equivalence Theorem, asymptotic design, arcsin distribution, D-optimal design
統計
Statistics
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中文摘要
在這篇論文中,探討d 維的多項式迴歸模型具權重函數Exp(α x),而D 最適設計 ξ_d^* 可藉由三個微分方程的式子完全刻畫出來,且一些轉換不變的性質也有推導並証明。當d 趨近於無窮大時,我們也證明此D 最適設計ξ_d^* 會弱收歛至arcsin 分布,且此篇論文也做了ξ_d^* 與arcsin 分布的比較。
Abstract
Weighted polynomial regression of degree d with weight function Exp(α x) on an interval is considered. The D-optimal designs ξ_d^* are completely characterized via three differential equations. Some invariant properties of ξ_d^* under affine transformation are derived. The design ξ_d^* as d goes to 1, is shown to converge weakly to the arcsin distribution. Comparisons of ξ_d^* with the arcsin distribution are also made.
目次 Table of Contents
Contents
Abstract ....................................................................ii
1 Introduction ..........................................................1
2 Preliminary ...........................................................2
3 Asymptotic distribution of ξ_d^* .......................4
4 Examples ..............................................................7
5 Conclusions .........................................................11
Appendix ...................................................................12
References ...............................................................14
參考文獻 References
References

Chang, F.-C. and Lin, G.-C. (1997). D-optimal designs for weighted polynomial regres-
sion. J. Statist. Plann. Inference 62, 317-331.

Fedorov, V.V. (1972). Theory of Optimal Experiments (Translated by W.J. Studden and
E.M. Klimko). Academic press, New York.

Hoel, P.G. (1958). E±ciency problems in polynomial estimation. Ann. Math. Statist.
29, 1134-1145.

Karlin, S. and Studden, W.J. (1966). Optimal experimental designs. Ann. Math. Statist.
37, 783-815.

Kiefer, J.C. andWolfowitz, J. (1960). The equivalence of two extremum problems. Canad.
J. Math. 12, 363-366.

Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (2002). Numerical
Recipes in C++, 2nd edition. Cambridge University Press, London.

Pukelsheim, F. (1993). Optimal Design of Experiments. Wiley, New York.

Silvey, S.D. (1980). Optimal Design. Chapman & Hall, London.

Szeg
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