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Optimal Design of Experiments

Optimal Design of Experiments

£84.00

Part of Classics in Applied Mathematics

  • Date Published: April 2006
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898716047

£ 84.00
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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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.

    • Suitable for anyone involved in planning statistical experiments, including mathematical statisticians, applied statisticians, and mathematicians interested in matrix optimization problems
    • Results are illustrated with optimal designs for many examples, including polynomial fit models, Bayes designs, exchangeable designs on the cube and rotatable designs on the sphere
    • This book offers a rare blend of linear algebra, convex analysis, and statistics
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    Product details

    • Date Published: April 2006
    • format: Paperback
    • isbn: 9780898716047
    • length: 184 pages
    • dimensions: 229 x 153 x 20 mm
    • weight: 0.527kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    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.

  • Author

    Friedrich Pukelsheim, Universit├Ąt Augsburg

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