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Optimal Design of Experiments

Framsida
0 Recensioner
SIAM, 1 apr 2006 - 454 sidor
Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer information matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples. Since the book's initial publication in 1993, readers have used its methods to derive optimal designs on the circle, optimal mixture designs, and optimal designs in other statistical models. Using local linearization techniques, the methods described in the book prove useful even for nonlinear cases, in identifying practical designs of experiments. Audience: anyone involved in planning statistical experiments, including mathematical statisticians, applied statisticians, and mathematicians interested in matrix optimization problems.
  

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Innehåll

Experimental Designs in Linear Models
1
Optimal Designs for Scalar Parameter Systems
35
Information Matrices
61
Loewner Optimality
98
Real Optimality Criteria
114
Matrix Means
135
The General Equivalence Theorem
158
Optimal Moment Matrices and Optimal Designs
187
Admissibility of Moment and Information Matrices
247
Bayes Designs and Discrimination Designs
268
Efficient Designs for Finite Sample Sizes
304
Kiefer Optimality
352
Rotatability and Response Surface Designs
406
Comments and References
408
Biographies
428
Copyright

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Optimal Design of Experiments
Optimal Design of Experiments
Friedrich Pukelsheim
Begränsad förhandsgranskning - 2006
Optimal design of experiments
Optimal design of experiments
Friedrich Pukelsheim
Begränsad förhandsgranskning - 1993
Optimal Design of Experiments
Optimal Design of Experiments
Friedrich Pukelsheim
Begränsad förhandsgranskning - 2006
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Vanliga ord och fraser

admissible arcsin support Bayes block design bound Chebyshev polynomials CK(A CK(M coefficient matrix coefficient vector competing moment matrices concave convex set Corollary defined design for sample design problem dispersion matrix eigenvector Elfving set entails equality Euclidean Exhibit exists experimental domain finite full column rank function f Gauss-Markov Theorem Hence Holder inequality information function information matrix mapping invariant inverse G isotonic Lagrange polynomials left inverse Lemma linear model Loewner optimal Loewner ordering matrix mean f>p maximizes minimizing NND(fc NND(s norm normality inequality nullspace obtain oo-optimal optimal design optimal for K'd optimal moment matrix optimal value orthogonal parameter system PD(s polarity equation polynomial fit models positive definite projector Proof properties Pukelsheim regression range regression vectors sample size scalar optimality scalar product Schur complement Section strictly isotonic subgradient subset subspace sum vector superadditive support points supporting hyperplane Sym(fc Sym(s symmetric trace MN weights yields

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Referenser från webbsidor

JSTOR: Optimal Design of Experiments
Optimal Design of Experiments, by Friedrich PUKELSHEIM, New York: John Wiley, 1993, xxiii + 454 pp., $69.95. The linear notes accurately state that this ...
links.jstor.org/ sici?sici=0040-1706(199405)36%3A2%3C214%3AODOE%3E2.0.CO%3B2-C

Global Optimization Problems in Optimal Design of Experiments in ...
In this paper we show that optimal design of experiments, a specific topic in statistics, constitutes a challenging application field for global ...
portal.acm.org/ citation.cfm?id=596356& jmp=cit& coll=GUIDE& dl=GUIDE& CFID=15151515& CFTOKEN=6184618

Journal of Statistical Planning and Inference : Optimal design of ...
Optimal design of experiments for modeling processes with feedback control .... The purpose of this paper is to study the optimal design of experiments for ...
linkinghub.elsevier.com/ retrieve/ pii/ S0378375801003056

Optimal Design of Experiments
Optimal Design of Experiments. Buy a book... In Association with Amazon.co.uk. Author(s): F. Pukelsheim. Publisher: SIAM. ISBN: 0898716047. Format: softback ...
www.booknews.co.uk/ Books/ Book4316.html

Robustness Aspects in Parameter Estimation, Optimal Design of ...
Parameter estimation and optimal design of experiments are important ...... Pukelsheim, P.: Optimal Design of Experiments. John Wiley & Sons, Inc., New ...
www.springerlink.com/ index/ h46180t77577p223.pdf

Friedrich Pukelsheim - Publikationen
a, Optimal Design of Experiments. Classics in Applied Mathematics, Volume 50, xxx + 454 Seiten. Society for Industrial and Applied Mathematics: Philadelphia ...
www.math.uni-augsburg.de/ stochastik/ pukelsheim/ publikationen.html

Optimal Design of Experiments for Modeling Processes with Feedback ...
Feedback control schemes have been widely used in many engineering applications for a long time. Despite this, there has been very little work done on ...
citeseer.ist.psu.edu/ xu99optimal.html

Blackwell Synergy - Aust nzj Stat, Volume 49 Issue 1 Page 109-110 ...
Optimal Design of Experiments. New York. : John Wiley & Sons. •. Schwabe, R. (1996). Optimum Designs for Multi-factor Models. Lecture Notes in Statistics ...
www.blackwell-synergy.com/ doi/ abs/ 10.1111/ j.1467-842X.2006.00460.x

Stat 591: Advanced Design of Experiments Rutgers University Fall ...
Contents. Lecture 1. Strategy of Experimentation I. 1. 1. Introduction. 1. 2. Stategy of Experimentation. 1. 3. Two Level Factorial Experiments ...
www.stat.rutgers.edu/ ~buyske/ 591/ lect_all.pdf

Ooptimal design of dose response experiments: A model-oriented ...
Pukelsheim F. Optimal Design of Experiments. New York, NY: Wiley; 1993. ... The Optimal Design of Experiments for Estimation in Nonlinear Model. ...
findarticles.com/ p/ articles/ mi_qa3899/ is_200110/ ai_n8958903/ pg_1

Om författaren (2006)

Friedrich Pukelsheim is Chair of Stochastics and Its Applications at the Institute for Mathematics, University of Augsburg, Germany. He is a member of the Institute of Mathematical Statistics, the International Statistical Institute, and Deutsche Mathematiker-Vereinigung. He serves as editor of MetrikaInternational Journal for Theoretical and Applied Statistics.

Bibliografisk information

QR code for Optimal Design of Experiments
TitelOptimal Design of Experiments
Volym 50 av Classics in Applied Mathematics
FörfattareFriedrich Pukelsheim
Utgåvaillustrerad, fullständig, nytryck
UtgivareSIAM, 2006
ISBN0898716047, 9780898716047
Längd454 sidor
  
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