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博碩士論文 etd-0728103-143737 詳細資訊
Title page for etd-0728103-143737
論文名稱
Title
混合實驗在Scheffe'模型之穩健A-最適設計
Robust A-optimal designs for mixture experiments in Scheffe' models
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
43
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
2003-06-06
繳交日期
Date of Submission
2003-07-28
關鍵字
Keywords
最適設計
equivalence theorem, invariant symmetric block matrices, robust design., Convex combination
統計
Statistics
本論文已被瀏覽 5737 次,被下載 1762
The thesis/dissertation has been browsed 5737 times, has been downloaded 1762 times.
中文摘要
在這文章中,我們對於混和實驗考慮在Scheffe(1958)的線性和二次模型中調查穩健A-最適設計. 在陳令由(2000),對於線性和二次模型的A-最適設計已經呈現,我們將利用在一些穩健的A最適方法的結果下,去發現一些線性和二次兩者的穩健設計.而這設計,也被證明會是線性和二次的最適設計的線性組合.
Abstract
A mixture experiment is an
experiments in which the q-ingredients are nonnegative
and subject to the simplex restriction on
the (q-1)-dimentional probability simplex. In this
work , we investigate the robust A-optimal designs for mixture
experiments with uncertainty on the linear, quadratic models
considered by Scheffe' (1958). In Chan (2000), a review on the
optimal designs including A-optimal designs are presented for
each of the Scheffe's linear and quadratic models. We will use
these results to find the robust A-optimal design for the linear
and quadratic models under some robust A-criteria. It is shown
with the two types of robust A-criteria defined here, there
exists a convex combination of the individual A-optimal designs
for linear and quadratic models respectively to be robust
A-optimal. In the end, we compare efficiencies of these optimal
designs with respect to different A-criteria.
目次 Table of Contents
Contents
1. Introduction
2. Preliminary
3. The robust A-optimal designs for Scheffe's linear and quadratic models
4. Relation functions of r and a
5. Summary and further works
參考文獻 References
[1] Box, G. E. P., and Draper, N. R. (1959). A Basis for the Selection of a Response Surface Design, Journal of the American Statistical Association,
54, 622-654.
[2] Chan, L. Y. (2000). Optimal Design for Experiments with Mixtures: A Survey. Communications in Statistions Instatistics-Theory and Methods,
29 (9 & 10), 2281-2312.
[3] Guan, Y., Chao, X. (1987). On the A-optimal Allocation
of Observations for the Generalized Simplex-Centroid Design (in
Chinese). Journal of Engineering Mathematics, 4(3), 33-39.
[4] Dette, H. (1990). A Generalization of D- and Ds-
Optimal Design in Polynomial Regression. The Annals of
Statistics. Vol. 18, No. 4, 1784-1804.
[5] Draper, N. R., Gaffke, N. and Pukelsheim, F. (1993) Rotatability of Cariance Surfaces and Moment
Matrices. Journal of Statistical Planning and Inference. 36,
347-356.
[6] Draper, N. R., Heiligers, B. and Pukelsheim, F. (2000). Kiffer Ordering of Simplex Designs for Second-Degree Mixture Models with four or more Ingredients. The Annals of Statistics, Vol. 28. No. 2,
578-590.
[7] Draper, N. R., Pukelsheim, F. (1999). Kiffer Ordering of Simplex Designs for first- and second-degree Mixture Models. Journal of Statistical Planning and Inference 79, 325-348.
[8] Draper, N. R., Pukelsheim, F. (1998). Mixture Models based
on Homogeneous Polynomials. Journal of Statistical Planning
and Inference 71, 303-311.
[9] Fedorov V. V. (1972). Theory of Optimal Experiments.
Translated and edited by W. J. Studden and E. M. Klimko. Academic
press, New York.
[10] Kiefer, J. (1961). Optimal Designs in Regression
Problems, II. Annals of Mathematical Statistics, Vol. 32,
Issue 1, 298-325.
[11] Klein, T. (2002). Invariant Sysmmetric Block Matrices
for the Design of Mixture Experiments. Institutfur
Mathematik, Universitat Augsburg, Report No. 443.
[12] Klein, T. (2002). Optimal Designs for Second-degree Kronecker Model Mixture
Experiments. it Institutfur Mathematik,
Universitat Augsburg, Report No. 444.
[13] Pukelshiem, F. (1993). Optimal Design of Experiments.
Wiley, New York.
[14] Scheffe, H. (1958). Experiments with Mixtures. Journal of the Royal Statistical Society Series
B 20, 344-360.
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