Design of Experiments in Nonlinear Models

Asymptotic Normality, Optimality Criteria and Small-Sample Properties

  • Luc Pronzato
  • Andrej Pázman
Part of the Lecture Notes in Statistics book series (LNS, volume 212)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Luc Pronzato, Andrej Pázman
    Pages 1-9
  3. Luc Pronzato, Andrej Pázman
    Pages 11-20
  4. Luc Pronzato, Andrej Pázman
    Pages 21-77
  5. Luc Pronzato, Andrej Pázman
    Pages 105-165
  6. Luc Pronzato, Andrej Pázman
    Pages 167-186
  7. Luc Pronzato, Andrej Pázman
    Pages 187-233
  8. Luc Pronzato, Andrej Pázman
    Pages 235-275
  9. Luc Pronzato, Andrej Pázman
    Pages 277-333
  10. Back Matter
    Pages 335-399

About this book

Introduction

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.

Keywords

Asymptotic Normality Experimental Design LS Estimator Non-Linear Regression Regression Model Small Sample Properties

Authors and affiliations

  • Luc Pronzato
    • 1
  • Andrej Pázman
    • 2
  1. 1., French National Center for Scientific ReUniversity of NiceSophia AnitpolisFrance
  2. 2., Department of Applied Mathematics and StComenius UniversityBratislavaSlovakia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-6363-4
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-6362-7
  • Online ISBN 978-1-4614-6363-4
  • Series Print ISSN 0930-0325