Optimal design of experiments / Friedrich Pukelsheim.

Format:

Book

Author/Creator:

Pukelsheim, Friedrich, 1948-

Contributor:

Society for Industrial and Applied Mathematics.

Series:

Classics in applied mathematics ; 50.

Classics in applied mathematics ; 50

Language:

English

Subjects (All):

Esperimental design.

Physical Description:

1 electronic text (xxix, 454 p. : ill.) : digital file.

Edition:

Classic ed.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2006.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

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.

Contents:

Experimental designs in linear models

Optimal designs for scalar parameter systems

Information matrices

Loewner optimality

Real optimality criteria

Matrix means

The general equivalence theorem

Optimal moment matrices and optimal designs

D-, A-, E-, T-optimality

Admissibility of moment and information matrices

Bayes designs and discrimination designs

Efficient designs for finite sample sizes

Invariant design problems

Kiefer optimality

Rotatability and response surface designs.

Notes:

Originally published: New York : J. Wiley, 1993.

Includes bibliographical references (p. 432-447) and index.

Description based on title page of print version.

ISBN:

0-89871-910-0

Publisher Number:

CL50 siam

CL50 SIAM