Statistical Regression with Measurement Error Kendall's Library of Statistics 6

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ISBN: 9780470711064 | 047071106X
Cover: Hardcover
Copyright: 6/28/2010

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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.

Preface
Introduction to Linear Measurement Error Models
Preliminaries
Elementary Properties of Measurement Error Models
Maximum Likelihood Estimation in the Univariate Normal Measurement Error Model
The ME Model with Correlated Errors
The Equation Error Model
The Berkson Model
Maximum Likelihood Estimation of Transformed Data: Elimination of Nuisance Parameters
Bibliographic Notes and Discussion
Exercises
Properties of Estimate and Predictors
Asymptotic Properties of ME Model Parameter Estimates
Asymptotic Properties of Equation Error Model Estimates
Finite-Sample Properties
Implications Regarding Confidence Regions
Prediction and Calibration under Measurement Error Models
Bibliographic Notes and Discussion
Exercises
Research Problems
Comparing Model Assumptions and Modifying Least Squares
Issues Facing Users of ME Models
A Unified Approach to the Functional, Structural, and Ultrastructural Relationships
Identifiability Assumptions and the Equation Error Model
Generalized Least Squares
Modified Least Squares
Bibliographic Notes and Discussion
Exercises
Alternative Approaches to the Measurement Error Model
Introduction and Overview
Instrumental Variable Estimators
Grouping Methods
Methods Based on Ranks
Methods of Higher-order Moments and Product Cumulants
Bibliographic Notes and Discussion
Exercises
Linear Measurement Error Model with Vector Explanatory Variables
Introduction
Identifiability
The Equation Error Model
Maximum Likelihood for the No-Equation-Error Model
Alternative Approaches to Estimating the Parameters
Asymptotic Properties of the Estimates
Bibliographic Notes and Discussion
Exercises
Research Problem
Polynomial Measurement Error Models
Introduction
The Nonlinear Structural Model
Identifiability in Nonlinear ME Models
Polynomial Model with Equation Error
The Polynomial Functional Relationship without Equation Error
Polynomial Berkson Model
Bibliographic Notes and Discussion
Exercises
Robust Estimation in Measurement Error Models
Introduction
Robust Orthogonal Regression
Robust Measurement Error Model Estimation via Robust Covariance Matrices
Computational Methods for Robust Orthogonal Regression
Bibliographic Notes and Discussion
Exercises
Research Problem
Additional Topics
Estimation of the True Variables
Obtaining Identifiability Assumption Information
Conclusions
Relations to Other Latent Variables Models
The factor analysis model
Terminology
Exercises
Identification in Measurement Error Models
Overview
Structural Model
Functional Model
Identiability and Consistent Estimation
Bibliography
Author Index
Subject Index
Table of Contents provided by Publisher. All Rights Reserved.

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Statistical Regression with Measurement Error Kendall's Library of Statistics 6

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Table of Contents

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Statistical Regression with Measurement Error Kendall's Library of Statistics 6

Summary

Author Biography

Table of Contents

Supplemental Materials

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