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Full Description
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.
Contents
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.
