Optimal Design of ExperimentsSIAM, 1 d’abr. 2006 - 483 pàgines 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. |
Altres edicions - Mostra-ho tot
Frases i termes més freqüents
admissible Annals of Statistics arcsin support Bayes bound Chebyshev Chebyshev polynomial Ck(A CK(M coefficient matrix competing moment matrices concave convex convex set D-optimal design for sample design of experiments design problem dispersion matrix eigenvalue Elfving set Equivalence Theorem estimator Euclidean Exhibit experimental designs experimental domain feasibility cone finite full column rank Gaffke Gauss-Markov Theorem Hence Hölder inequality information function information matrix information matrix mapping invariant inverse G isotonic Journal of Statistical Kiefer optimal left inverse Lemma linear model Loewner optimal Loewner ordering matrix means maximal moment matrix monotonicity NND(k NND(s normality inequality nullspace optimal design optimality criterion orthogonal parameter system parameter vector PD(s polarity equation polynomial fit models positive definite Proof properties Pukelsheim regression range regression vectors rotatable sample size satisfies scalar optimality Schur complement Section Studden subgradient subset subspace subsystem superadditive support points Sym(k Sym(s theory variance vector weights yields