Optimal Design of Experiments

Friedrich Pukelsheim9780898716047, 0898716047

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 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 This book is indispensable for anyone involved in planning statistical experiments, including mathematical statisticians, applied statisticians, and mathematicians interested in matrix optimization problems.

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Table of contents :
Optimal Design of Experiments……Page 1
Contents……Page 8
Preface to the Classics Edition……Page 18
Preface……Page 20
List of Exhibits……Page 22
Interdependence of Chapters……Page 25
Outline of the Book……Page 26
Errata……Page 30
C H A P T E R 1 Experimental Designs in Linear Models……Page 34
C H A P T E R 2 Optimal Designs for Scalar Parameter Systems……Page 68
CHAPTER 3 Information Matrices……Page 94
C H A P T E R 4 Loewner Optimality……Page 131
C H A P T E R 5 Real Optimality Criteria……Page 147
C H A P T E R 6 Matrix Means……Page 168
C H A P T E R 7 The General Equivalence Theorem……Page 191
C H A P T E R 8 Optimal Moment Matrices and Optimal Designs……Page 220
C H A P T E R 9 D-, A-, E-, T-Optimality……Page 243
C H A P T E R 10 Admissibility of Moment and Information Matrices……Page 280
C H A P T E R 11 Bayes Designs and Discrimination Designs……Page 301
C H A P T E R 12 Efficient Designs for Finite Sample Sizes……Page 337
C H A P T E R 13 Invariant Design Problems……Page 364
C H A P T E R 14 Kiefer Optimality……Page 385
C H A P T E R 15 Rotatability and Response Surface Designs……Page 414
Comments and References……Page 441
Biographies……Page 461
Bibliography……Page 465
Subject Index……Page 481