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Lecture Notes in Statistics

Design of Experiments in Nonlinear Models

Asymptotic Normality, Optimality Criteria and Small-Sample Properties

Authors: Pronzato, Luc, Pázman, Andrej

  • Covers many important aspects of experimental design, especially as it relates to unpredictable models and data sets
  • Special section on small samples sizes and missing/truncated and imputed data
  • Provides information on small sample size, asymptotic normality, and optimality criteria
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eBook $109.00
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  • ISBN 978-1-4614-6363-4
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  • ISBN 978-1-4614-6362-7
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About this book

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.

About the authors

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).

Reviews

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)

Table of contents (9 chapters)

  • Introduction

    Pronzato, Luc (et al.)

    Pages 1-9

  • Asymptotic Designs and Uniform Convergence

    Pronzato, Luc (et al.)

    Pages 11-20

  • Asymptotic Properties of the LS Estimator

    Pronzato, Luc (et al.)

    Pages 21-77

  • Asymptotic Properties of M, ML, and Maximum A Posteriori Estimators

    Pronzato, Luc (et al.)

    Pages 79-104

  • Local Optimality Criteria Based on Asymptotic Normality

    Pronzato, Luc (et al.)

    Pages 105-165

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-6363-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $149.00
price for USA
  • ISBN 978-1-4614-6362-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Design of Experiments in Nonlinear Models
Book Subtitle
Asymptotic Normality, Optimality Criteria and Small-Sample Properties
Authors
Series Title
Lecture Notes in Statistics
Series Volume
212
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-6363-4
DOI
10.1007/978-1-4614-6363-4
Softcover ISBN
978-1-4614-6362-7
Series ISSN
0930-0325
Edition Number
1
Number of Pages
XV, 399
Number of Illustrations and Tables
19 b/w illustrations, 37 illustrations in colour
Topics