Optimal Design of ExperimentsSIAM, 1 jan. 1993 - 483 sidor 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 information 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. Audience: anyone involved in planning statistical experiments, including mathematical statisticians, applied statisticians, and mathematicians interested in matrix optimization problems. |
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admissibility applies assume assumption block design bound called CK(M closed coefficient column compact competing condition cone continuous converse convex criteria criterion defined design problem determinant direct discussed distribution domain efficiency eigenvalue Elfving equality equation Equivalence Theorem establish estimator example Exhibit exists experimental factor feasibility first fit model follows given Hence holds implies includes information function information matrix interest invariant inverse Kiefer leads Lemma linear Loewner mapping matrix means maximizes mean minimizing moment matrix NND(k NND(s nonnegative definite normality inequality obtain optimal design orthogonal parameter polarity polynomial fit positive positive definite present proof properties provides Pukelsheim range rank regression range relation relative result rotatable sample sample size satisfies scalar Section space Statistics subgradient support points Sym(s symmetric Theorem theory tion trace unique variance vector weights yields