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Other titles in the Springer Optimization and Its Applications series:
Springer Optimization and Its Applications #50: Optimal Design and Related Areas in Optimization and Statisticsby Luc Pronzato
Synopses & Reviews
This edited volume, dedicated to Henry P. Wynn, reflects his broad range of research interests, focusing in particular on the applications of optimal design theory in optimization and statistics. It covers algorithms for constructing optimal experimental designs, general gradient-type algorithms for convex optimization, majorization and stochastic ordering, algebraic statistics, Bayesian networks and nonlinear regression. Written by leading specialists in the field, each chapter contains a survey of the existing literature along with substantial new material. This work will appeal to both the specialist and the non-expert in the areas covered. By attracting the attention of experts in optimization to important interconnected areas, it should help stimulate further research with a potential impact on applications.
This volume is a collective monograph devoted to applications of the optimal design theory in optimization and statistics. The chapters reflect 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 workshop acknowledged the work and influence of statistics scholar Henry P. Wynn, who is also a contributor. Reflecting the wide spectrum of his research interests and contributions, the topics explore algorithmic construction of optimal designs, asymptotic properties of general gradient algorithms for convex optimization, algebraic statistics and its sub-areas, and nonlinear regression. Each chapter reviews, analyzes, and extends the statistical literature with rigor and clarity.
This volume provides review material as well as the beginnings of new questions and fields that need continuing research efforts. It will be of interest to both specialist and non-expert in the areas covered.
Dedicated to Henry P. Wynn, this edited volume reflects his broad range of research interests, focusing in particular on the applications of optimal design theory in optimization and statistics. Chapters survey the existing literature and contain new material.
Table of Contents
Preface.- B. Torsney: W-iterations and Ripples Therefrom.- R. Haycroft, L. Pronzato, H.P. Wynn, A. Zhigljavsky: Studying Convergence of Gradient Algorithms via Optimal Experimental Design Theory.- L. Pronzato, H.P. Wynn, A. Zhigljavsky: A Dynamical-System Analysis of the Optimum S-Gradient Algorithm.- A. Giovagnoli, J. Marzialetti, H.P. Wynn: Bivariate Dependence Orderings for Unordered Categorical Variables.- G. Pistone, E. Riccomagno, M.P. Rogantin: Methods in Algebraic Statistics for the Design of Experiments.- E. Riccomagno, J.Q. Smith:The Geometry of Causal Probability Trees that are Algebraically Constrained.- P.E. Caines, R. Deardon, H.P. Wynn: Bayes Nets of Time Series: Stochastic Realisations and Projections.- A. Pazman, L. Pronzato: Asymptotic Normality of Nonlinear Least Squares under Singular Experimental Designs.- A. Ivanov, N. Leonenko: Robust Estimators in Nonlinear Regression Models with Long-Range Dependence.- Index.
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