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博碩士論文 etd-0722102-151846 詳細資訊
Title page for etd-0722102-151846
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
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
18
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
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
統計
Statistics
本論文已被瀏覽 5732 次,被下載 1481
The thesis/dissertation has been browsed 5732 times, has been downloaded 1481 times.
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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