Responsive image
博碩士論文 etd-0606102-142718 詳細資訊
Title page for etd-0606102-142718
論文名稱
Title
交換式演算法建構連續最適設計
Construction of approximate optimal designs by exchange algorithm
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
21
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
2001-06-01
繳交日期
Date of Submission
2002-06-06
關鍵字
Keywords
連續最適設計、離散最適設計、A-最優、交換式演算法、D-最優
D-optima, approximate, exact, exchange algorithm
統計
Statistics
本論文已被瀏覽 5690 次,被下載 4202
The thesis/dissertation has been browsed 5690 times, has been downloaded 4202 times.
中文摘要
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。
Abstract
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.
目次 Table of Contents
Abstract..............................1
Introduction..........................3
Preliminary...........................4
Algorithms............................7
tem Examples and simulation results...10
Conclusiondotfill....................13
Reference
參考文獻 References
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.

電子全文 Fulltext
本電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。
論文使用權限 Thesis access permission:校內校外完全公開 unrestricted
開放時間 Available:
校內 Campus: 已公開 available
校外 Off-campus: 已公開 available


紙本論文 Printed copies
紙本論文的公開資訊在102學年度以後相對較為完整。如果需要查詢101學年度以前的紙本論文公開資訊,請聯繫圖資處紙本論文服務櫃台。如有不便之處敬請見諒。
開放時間 available 已公開 available

QR Code