Design of Experiments in Nonlinear Models
Asymptotic Normality, Optimality Criteria and Small-Sample Properties
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Beschreibung
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.
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.
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
Autor*in
Luc Pronzato
Themen in »Design of Experiments in Nonlinear Models«
Asymptotic Normality Experimental Design LS Estimator Non-Linear Regression Regression Model Small Sample Properties
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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)()