Optimal Design of Experiments

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.This book is indispensable for anyone involved in planning statistical experiments, including mathematical statisticians, applied statisticians, and mathematicians interested in matrix optimization problems.Preface; Chapter 1: Experimental Designs in Linear Models; Chapter 2: Optimal Designs for Scalar Parameter Systems; Chapter 3: Information Matrices; Chapter 4: Loewner Optimality; Chapter 5: Real Optimality Criteria; Chapter 6: Matrix Means; Chapter 7: The General Equivalence Theorem; Chapter 8: Optimal Moment Matrices and Optimal Designs; Chapter 9: D-, A-, E-, T-Optimality; Chapter 10: Admissibility of Moment and Information Matrices; Chapter 11: Bayes Designs and Discrimination Designs; Chapter 12: Efficient Designs for Finite Sample Sizes; Chapter 13: Invariant Design Problems; Chapter 14: Kiefer Optimality; Chapter 15: Rotatability and Response Surface Designs; Comments and References; Biographies; Bibliography; Index. More

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 Metrika—International Journal for Theoretical and Applied Statistics.