Design of Experiments in Nonlinear Models : Asymptotic Normality, Optimality Criteria and Small-Sample Properties
Luc. Pronzato
Bok Engelsk 2013 · Electronic books.
| Annen tittel | |
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| Utgitt | New York, N.Y. : Springer , c2013
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| Omfang | 1 online resource (399 p.)
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| Opplysninger | Description based upon print version of record.. - Preface; Contents; 1 Introduction; 1.1 Experiments and Their Designs; 1.2 Models; 1.3 Parameters; 1.4 Information and Design Criteria; 2 Asymptotic Designs and Uniform Convergence; 2.1 Asymptotic Designs; 2.2 Uniform Convergence; 2.3 Bibliographic Notes and Further Remarks; 3 Asymptotic Properties of the LS Estimator; 3.1 Asymptotic Properties of the LS Estimator in Regression Models; 3.1.1 Consistency; 3.1.2 Consistency Under a Weaker LS EstimabilityCondition; 3.1.3 Asymptotic Normality; 3.1.4 Asymptotic Normality of a Scalar Function of the LS Estimator. - 3.2 Asymptotic Properties of Functions of the LS Estimator Under Singular Designs3.2.1 Singular Designs in Linear Models; 3.2.2 Singular Designs in Nonlinear Models; Regular Asymptotic Normality when X is Finite; Regular Asymptotic Normality when ""705ELSN is not Consistent; Regular Asymptotic Normality of a Multidimensional Function h; 3.3 LS Estimation with Parameterized Variance; 3.3.1 Inconsistency of WLS with Parameter-Dependent Weights; 3.3.2 Consistency and Asymptotic Normality of Penalized WLS; 3.3.3 Consistency and Asymptotic Normalityof Two-stage LS. - 3.3.4 Consistency and Asymptotic Normality of Iteratively Reweighted LS3.3.5 Misspecification of the Variance Function; 3.3.6 Different Parameterizations for the Meanand Variance; Penalized WLS Estimation; Two-stage LS Estimation; 3.3.7 Penalized WLS or Two-Stage LS?; Normal Errors; No Common Parameters in the Mean and Variance Functions; Non-normal Errors; Bernoulli Experiments; 3.3.8 Variance Stabilization; 3.4 LS Estimation with Model Error; 3.5 LS Estimation with Equality Constraints; 3.6 Bibliographic Notes and Further Remarks. - 4 Asymptotic Properties of M, ML, and Maximum A Posteriori Estimators4.1 M Estimators in Regression Models; 4.2 The Maximum Likelihood Estimator; 4.2.1 Regression Models; 4.2.2 General Situation; 4.3 Generalized Linear Models and Exponential Families; 4.3.1 Models with a One-Dimensional Sufficient Statistic; 4.3.2 Models with a Multidimensional Sufficient Statistic; 4.4 The Cramér-Rao Inequality: Efficiency of Estimators; 4.4.1 Efficiency; 4.4.2 Asymptotic Efficiency; 4.5 The Maximum A Posteriori Estimator; 4.6 Bibliographic Notes and Further Remarks. - 5 Local Optimality Criteria Based on AsymptoticNormality5.1 Design Criteria and Their Properties; 5.1.1 Ellipsoid of Concentration; 5.1.2 Classical Design Criteria; 5.1.3 Positive Homogeneity, Concavity, and Isotonicity; 5.1.4 Equivalence Between Criteria; 5.1.5 Concavity and Isotonicity of Classical Criteria; 5.1.6 Classification into Global and Partial Optimality Criteria; 5.1.7 The Upper Semicontinuity of the c-OptimalityCriterion; 5.1.8 Efficiency; 5.1.9 Combining Criteria; Compound Criteria; Using Design Criteria as Constraints; 5.1.10 Design with a Cost Constraint. - 5.2 Derivatives and Conditions for Optimality of Designs. - 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,
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 9781461463627
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