Optimal Design and Related Areas in Optimization and Statistics

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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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.

• Bayesian networks
• SOIA
• algebraic statistics
• algorithms
• gradient-type algorithms
• linear optimization
• optimal design theory
• optimization
• algorithm analysis and problem complexity

• 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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