Statistical Regression with Measurement Error
Kendall's Library of Statistics 6
1st Edition
Published on 26. February 1999
Book
Hardback
282 pages
978-0-470-71106-4 (ISBN)
Description
Providing a general survey of the theory of measurement error models, including the functional, structural, and ultrastructural models, this book is written in the of the Kendall and Stuart Advanced Theory of Statistics set and, like that series, includes exercises at the end of the chapters. The goal is to emphasize the ideas and practical implications of the theory in a style that does not concentrate on the theorem-proof format.
More details
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 20 mm
Weight
592 gr
ISBN-13
978-0-470-71106-4 (9780470711064)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
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Previous edition
John W.Van Ness | Chi-Lun Cheng
Statistical Regression with Measurement Error
Book
02/1999
Hodder Arnold
€80.60
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Persons
Chi-Lun Cheng and John W. Van Ness are the authors of Statistical Regression with Measurement Error: Kendall's Library of Statistics 6, published by Wiley.
Content
Preface. 1. Introduction to Linear Measurement Error Models.
1.1 Preliminaries.
1.2 Elementary Properties of Measurement Error Models.
1.3 Maximum Likelihood Estimation in the Univariate Normal Measurement Error Model.
1.4 The ME Model with Correlated Errors.
1.5 The Equation Error Model.
1.6 The Berkson Model.
1.7 Maximum Likelihood Estimation of Transformed Data: Elimination of Nuisance Parameters.
1.8 Bibliographic Notes and Discussion.
1.9 Exercises.
2. Properties of Estimate and Predictors.
2.1 Asymptotic Properties of ME Model Parameter Estimates.
2.2 Asymptotic Properties of Equation Error Model Estimates.
2.3 Finite-Sample Properties.
2.4 Implications Regarding Confidence Regions.
2.5 Prediction and Calibration under Measurement Error Models.
2.6 Bibliographic Notes and Discussion.
2.7 Exercises.
2.8 Research Problems.
3. Comparing Model Assumptions and Modifying Least Squares.
3.1 Issues Facing Users of ME Models.
3.2 A Unified Approach to the Functional, Structural, and Ultrastructural Relationships.
3.3 Identifiability Assumptions and the Equation Error Model.
3.4 Generalized Least Squares.
3.5 Modified Least Squares.
3.6 Bibliographic Notes and Discussion.
3.7 Exercises.
4. Alternative Approaches to the Measurement Error Model.
4.1 Introduction and Overview.
4.2 Instrumental Variable Estimators.
4.3 Grouping Methods.
4.4 Methods Based on Ranks.
4.5 Methods of Higher-order Moments and Product Cumulants.
4.6 Bibliographic Notes and Discussion.
4.7 Exercises.
5. Linear Measurement Error Model with Vector Explanatory Variables.
5.1 Introduction.
5.2 Identifiability
5.3 The Equation Error Model.
5.4 Maximum Likelihood for the No-Equation-Error Model.
5.5 Alternative Approaches to Estimating the Parameters.
5.6 Asymptotic Properties of the Estimates.
5.7 Bibliographic Notes and Discussion.
5.8 Exercises.
5.9 Research Problem.
6. Polynomial Measurement Error Models.
6.1 Introduction.
6.2 The Nonlinear Structural Model.
6.3 Identifiability in Nonlinear ME Models.
6.4 Polynomial Model with Equation Error.
6.5 The Polynomial Functional Relationship without Equation Error.
6.6 Polynomial Berkson Model.
6.7 Bibliographic Notes and Discussion.
6.8 Exercises.
7. Robust Estimation in Measurement Error Models.
7.1 Introduction.
7.2 Robust Orthogonal Regression.
7.3 Robust Measurement Error Model Estimation via Robust Covariance Matrices.
7.4 Computational Methods for Robust Orthogonal Regression.
7.5 Bibliographic Notes and Discussion.
7.7 Exercises.
7.8 Research Problem.
8. Additional Topics.
8.1 Estimation of the True Variables.
8.2 Obtaining Identifiability Assumption Information.
8.3 Conclusions.
8.4 Relations to Other Latent Variables Models.
8.5 The factor analysis model.
8.6 Terminology.
8.7 Exercises.
Appendix A. Identification in Measurement Error Models.
A.1 Overview.
A.2 Structural Model.
A.3 Functional Model.
A.4 Identiability and Consistent Estimation.
Bibliography.
Author Index.
Subject Index.
1.1 Preliminaries.
1.2 Elementary Properties of Measurement Error Models.
1.3 Maximum Likelihood Estimation in the Univariate Normal Measurement Error Model.
1.4 The ME Model with Correlated Errors.
1.5 The Equation Error Model.
1.6 The Berkson Model.
1.7 Maximum Likelihood Estimation of Transformed Data: Elimination of Nuisance Parameters.
1.8 Bibliographic Notes and Discussion.
1.9 Exercises.
2. Properties of Estimate and Predictors.
2.1 Asymptotic Properties of ME Model Parameter Estimates.
2.2 Asymptotic Properties of Equation Error Model Estimates.
2.3 Finite-Sample Properties.
2.4 Implications Regarding Confidence Regions.
2.5 Prediction and Calibration under Measurement Error Models.
2.6 Bibliographic Notes and Discussion.
2.7 Exercises.
2.8 Research Problems.
3. Comparing Model Assumptions and Modifying Least Squares.
3.1 Issues Facing Users of ME Models.
3.2 A Unified Approach to the Functional, Structural, and Ultrastructural Relationships.
3.3 Identifiability Assumptions and the Equation Error Model.
3.4 Generalized Least Squares.
3.5 Modified Least Squares.
3.6 Bibliographic Notes and Discussion.
3.7 Exercises.
4. Alternative Approaches to the Measurement Error Model.
4.1 Introduction and Overview.
4.2 Instrumental Variable Estimators.
4.3 Grouping Methods.
4.4 Methods Based on Ranks.
4.5 Methods of Higher-order Moments and Product Cumulants.
4.6 Bibliographic Notes and Discussion.
4.7 Exercises.
5. Linear Measurement Error Model with Vector Explanatory Variables.
5.1 Introduction.
5.2 Identifiability
5.3 The Equation Error Model.
5.4 Maximum Likelihood for the No-Equation-Error Model.
5.5 Alternative Approaches to Estimating the Parameters.
5.6 Asymptotic Properties of the Estimates.
5.7 Bibliographic Notes and Discussion.
5.8 Exercises.
5.9 Research Problem.
6. Polynomial Measurement Error Models.
6.1 Introduction.
6.2 The Nonlinear Structural Model.
6.3 Identifiability in Nonlinear ME Models.
6.4 Polynomial Model with Equation Error.
6.5 The Polynomial Functional Relationship without Equation Error.
6.6 Polynomial Berkson Model.
6.7 Bibliographic Notes and Discussion.
6.8 Exercises.
7. Robust Estimation in Measurement Error Models.
7.1 Introduction.
7.2 Robust Orthogonal Regression.
7.3 Robust Measurement Error Model Estimation via Robust Covariance Matrices.
7.4 Computational Methods for Robust Orthogonal Regression.
7.5 Bibliographic Notes and Discussion.
7.7 Exercises.
7.8 Research Problem.
8. Additional Topics.
8.1 Estimation of the True Variables.
8.2 Obtaining Identifiability Assumption Information.
8.3 Conclusions.
8.4 Relations to Other Latent Variables Models.
8.5 The factor analysis model.
8.6 Terminology.
8.7 Exercises.
Appendix A. Identification in Measurement Error Models.
A.1 Overview.
A.2 Structural Model.
A.3 Functional Model.
A.4 Identiability and Consistent Estimation.
Bibliography.
Author Index.
Subject Index.