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

✍ Scribed by Luc Pronzato, Andrej Pázman (auth.)

• Publisher: Springer-Verlag New York
• Year: 2013
• Tongue: English
• Leaves: 404
• Series: Lecture Notes in Statistics 212
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xv
Introduction....Pages 1-9
Asymptotic Designs and Uniform Convergence....Pages 11-20
Asymptotic Properties of the LS Estimator....Pages 21-77
Asymptotic Properties of M, ML, and Maximum A Posteriori Estimators....Pages 79-104
Local Optimality Criteria Based on Asymptotic Normality....Pages 105-165
Criteria Based on the Small-Sample Precision of the LS Estimator....Pages 167-186
Identifiability, Estimability, and Extended Optimality Criteria....Pages 187-233
Nonlocal Optimum Design....Pages 235-275
Algorithms: A Survey....Pages 277-333
Back Matter....Pages 335-399

✦ Subjects

Statistics for Life Sciences, Medicine, Health Sciences; Statistics, general; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law