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Optimal Design and Related Areas in Optimization and Statistics

  • Book
  • © 2009

Overview

Editors:
  1. Luc Pronzato

    1. CNRS/Université de Nice Sophia Antipolis Laboratoire 13S, Bât Euclide, Les Algorithmes, Sophia-Antipolis cedex, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Anatoly Zhigljavsky

    1. Cardiff University, School of Mathematics, Cardiff, United Kingdom

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    You can also search for this editor in PubMed   Google Scholar

  • Devoted to applications of the optimal design theory in optimization and statistics
  • Provides comprehensive surveys written by leading generalists
  • Each chapter reviews, analyzes, and extends the statistical literature with rigor and clarity
  • Establishes links between optimization and various areas in experimental design and statistics, including optimal experimental design, majorization and stochastic ordering, algebraic statistics, Bayesian networks, and nonlinear regression
  • Uncovers new applications of optimization to experimental design and statistics
  • Develops new optimization techniques based on ideas from experimental design and statistics
  • Acknowledges the work and influence of statistics scholar Henry P. Wynn

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 28)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XV
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  2. W-Iterations and Ripples Therefrom

    • B. Torsney
    Pages 1-12

  3. Studying Convergence of Gradient Algorithms Via Optimal Experimental Design Theory

    • R. Haycroft, L. Pronzato, H. P. Wynn, A. Zhigljavsky
    Pages 13-37

  4. A Dynamical-System Analysis of the Optimum s-Gradient Algorithm

    • L. Pronzato, H.P. Wynn, A. Zhigljavsky
    Pages 39-80

  5. Bivariate Dependence Orderings for Unordered Categorical Variables

    • A. Giovagnoli, J. Marzialetti, H. P. Wynn
    Pages 81-96

  6. Methods in Algebraic Statistics for the Design of Experiments

    • G. Pistone, E. Riccomagno, M. P. Rogantin
    Pages 97-132

  7. The Geometry of Causal Probability Trees that are Algebraically Constrained

    • E. Riccomagno, J. Q. Smith
    Pages 133-154

  8. Bayes Nets of Time Series: Stochastic Realizations and Projections

    • P. E. Caines, R. Deardon, H. P. Wynn
    Pages 155-166

  9. Asymptotic Normality of Nonlinear Least Squares under Singular Experimental Designs

    • A. Pázman, L. Pronzato
    Pages 167-191

  10. Robust Estimators in Non-linear Regression Models with Long-Range Dependence

    • A. Ivanov, N. Leonenko
    Pages 193-221

  11. Back Matter

    Pages 223-224
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Keywords

About this book

The present volume is a collective monograph devoted to applications of the optimal design theory in optimization and statistics. The chapters re?ect the topics discussed at the workshop “W-Optimum Design and Related Statistical Issues” that took place in Juan-les-Pins, France, in May 2005. The title of the workshop was chosen as a light-hearted celebration of the work of Henry Wynn. It was supported by the Laboratoire I3S (CNRS/Universit´ e de Nice, Sophia Antipolis), to which Henry is a frequent visitor. The topics covered partly re?ect the wide spectrum of Henry’s research - terests. Algorithms for constructing optimal designs are discussed in Chap. 1, where Henry’s contribution to the ?eld is acknowledged. Steepest-ascent - gorithms used to construct optimal designs are very much related to general gradientalgorithmsforconvexoptimization. Inthelasttenyears,asigni?cant part of Henry’s research was devoted to the study of the asymptotic prop- ties of such algorithms. This topic is covered by Chaps. 2 and 3. The work by Alessandra Giovagnoli concentrates on the use of majorization and stoch- tic ordering, and Chap. 4 is a hopeful renewal of their collaboration. One of Henry’s major recent interests is what is now called algebraic statistics, the application of computational commutative algebra to statistics, and he was partly responsible for introducing the experimental design sub-area, reviewed in Chap. 5. One other sub-area is the application to Bayesian networks and Chap. 6 covers this, with Chap. 7 being strongly related.

Editors and Affiliations

  • CNRS/Université de Nice Sophia Antipolis Laboratoire 13S, Bât Euclide, Les Algorithmes, Sophia-Antipolis cedex, France

    Luc Pronzato

  • Cardiff University, School of Mathematics, Cardiff, United Kingdom

    Anatoly Zhigljavsky

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