Design of Experiments in Nonlinear Models - Asymptotic Normality, Optimality Criteria and Small-Sample Properties

Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties provides a comprehensive coverage of the various aspects of experimental design for nonlinear models. The book contains original contributions to the theory of optimal experiments that will interest students and researchers in the field. Practitionners motivated by applications will find valuable tools to help them designing their experiments.
The first three chapters expose the connections between the asymptotic properties of estimators in parametric models and experimental design, with more emphasis than usual on some particular aspects like the estimation of a nonlinear function of the model parameters, models with heteroscedastic errors, etc. Classical optimality criteria based on those asymptotic properties are then presented thoroughly in a special chapter.
Three chapters are dedicated to specific issues raised by nonlinear models. The construction of design criteria derived from non-asymptotic considerations (small-sample situation) is detailed. The connection between design and identifiability/estimability issues is investigated. Several approaches are presented to face the problem caused by the dependence of an optimal design on the value of the parameters to be estimated.
A survey of algorithmic methods for the construction of optimal designs is provided.

List of contents

Introduction.- Asymptotic designs and uniform convergence. Asymptotic properties of the LS estimator.- Asymptotic properties of M, ML and maximum a posteriori estimators.- Local optimality criteria based on asymptotic normality.- Criteria based on the small-sample precision of the LS estimator.- Identifiability, estimability and extended optimality criteria.- Nonlocal optimum design.- Algorithms-a survey.- Subdifferentials and subgradients.- Computation of derivatives through sensitivity functions.- Proofs.- Symbols and notation.- List of labeled assumptions.- References.

About the author

Luc Pronzato is Directeur de Recherche at CNRS (French National Center for Scientific Research). From 2008 to 2011 he directed the I3S Laboratory (Informatique, Signaux et Systèmes, Sophia-Antipolis), University of Nice-Sophia-Antipolis/CNRS, where he is still working. He his the co-author of the books Identification of Parametric Models from Experimental Data (with Eric Walter, Springer, 1997) and Dynamical Search: Applications of Dynamical Systems in Search and Optimization (with Henry P. Wynn and Anatoly A. Zhigljavsky, Chapman & Hall/CRC Press, 2000). 
Andrej P\'azman is Professor of Probability and Statistics at the Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Slovakia. He has been Head of the Department of Probability and Statistics (1992-1998) and Head of the Section of Mathematics of his faculty (1999-2001), and he is an elected member of the Learned Society of the Slovak Academy of Sciences. He is the author of the books Foundations of Optimum Experimental Design (Reidel, Kluwer group, 1986) and Nonlinear Statistical Models (Kluwer, 1993).

Summary

Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties provides a comprehensive coverage of the various aspects of experimental design for nonlinear models. The book contains original contributions to the theory of optimal experiments that will interest students and researchers in the field. Practitionners motivated by applications will find valuable tools to help them designing their experiments. 
The first three chapters expose the connections between the asymptotic properties of estimators in parametric models and experimental design, with more emphasis than usual on some particular aspects like the estimation of a nonlinear function of the model parameters, models with heteroscedastic errors, etc. Classical optimality criteria based on those asymptotic properties are then presented thoroughly in a special chapter. 
Three chapters are dedicated to specific issues raised by nonlinear models. The construction of design criteria derived from non-asymptotic considerations (small-sample situation) is detailed. The connection between design and identifiability/estimability issues is investigated. Several approaches are presented to face the problem caused by the dependence of an optimal design on the value of the parameters to be estimated. 
A survey of algorithmic methods for the construction of optimal designs is provided.

Additional text

From the reviews:
“This book introduce basic concepts and discuss asymptotic properties of estimators in nonlinear models. … a major emphasis of the book is on deriving the asymptotic properties of estimators from properties of the experimental design. … this book covers a wealth of material, including algorithms for finding optimum designs. I believe this book is an excellent reference for researchers. It also might be suitable for an advanced graduate course.” (William I. Notz, Mathematical Reviews, March, 2014)

Report

From the reviews:
"This book introduce basic concepts and discuss asymptotic properties of estimators in nonlinear models. ... a major emphasis of the book is on deriving the asymptotic properties of estimators from properties of the experimental design. ... this book covers a wealth of material, including algorithms for finding optimum designs. I believe this book is an excellent reference for researchers. It also might be suitable for an advanced graduate course." (William I. Notz, Mathematical Reviews, March, 2014)

Product details

• Authors: Andrej P. Zman, Andrej Pazman, Andrej Pázman, Lu Pronzato, Luc Pronzato
• Assisted by: Luc Pronzato (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 18.12.2012
• EAN: 9781461463627
• ISBN: 978-1-4614-6362-7
• No. of pages: 399
• Dimensions: 155 mm x 19 mm x 234 mm
• Weight: 654 g
• Illustrations: XV, 399 p. 56 illus., 37 illus. in color.
• Series: Lecture Notes in Statistics; Lecture Notes in Statistics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics