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.

Preface; 1. Experimental designs in linear models; 2. Optimal designs for scalar parameter systems; 3. Information matrices; 4. Loewner optimality; 5. Real optimality criteria; 6. Matrix means; 7. The general equivalence theorem; 8. Optimal moment matrices and optimal designs; 9. D-, A-, E-, T-Optimality; 10. Admissibility of moment and information matrices; 11. Bayes designs and discrimination designs; 12. Efficient designs for finite sample sizes; 13. Invariant design problems; 14. Kiefer optimality; 15. Rotatability and response surface designs; Comments and references; Biographies; Bibliography; Index.

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.