Description - Optimal Design of Experiments by Friedrich Pukelsheim
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.
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(229mm x 152mm x 20mm)
Society for Industrial & Applied Mathematics,U.S.
Publisher: Society for Industrial & Applied Mathematics,U.S.
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Book Reviews - Optimal Design of Experiments by Friedrich Pukelsheim
Author Biography - Friedrich Pukelsheim
Friedrich Pukelsheim is Chair for Stochastics and Its Applications at the Institute for Mathematics, University of Augsburg, Germany. He i member of the Institute of Mathematical Statistics, the International Statistical Institute, and Deutsche Mathematiker-Vereinigung