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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.
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Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. 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.From the Publisher:
Devoted to a unified optimality theory, merging three otherwise distinct mathematical disciplines to embrace an astonishingly wide variety of design problems. Outlines typical settings, namely D-, A-, and E-optimal, polynominal regression designs, Bayesian designs, structures for model discrimination, balanced incomplete block arrangements or rotatable response surface designs. The design problems stem from statistics but are solved using special tools from linear algebra and convex analysis.
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Book Description Society for Industrial and Applied Mathematic, 2006. Paperback. Condition: New. Seller Inventory # DADAX0898716047
Book Description Brand: Society for Industrial and Applied Mathematic, 2006. Paperback. Condition: BRAND NEW. Seller Inventory # 0898716047_abe_bn
Book Description Society for Industrial & Applied, 2006. Paperback. Condition: Brand New. classic ed edition. 454 pages. 8.75x6.00x0.75 inches. In Stock. Seller Inventory # zk0898716047