Measurement error models /
Wayne A. Fuller.
New York : Wiley, 1987.
xxiii, 440 p. : ill. --
0471861871 :
More Details
New York : Wiley, 1987.
0471861871 :
general note
Includes index.
catalogue key
Bibliography: p. 409-432.
A Look Inside
About the Author
Author Affiliation
Wayne A. Fuller, PhD, is Distinguished Professor Emeritus in the Department of Economics at Iowa State University
This item was reviewed in:
SciTech Book News, December 1987
To find out how to look for other reviews, please see our guides to finding book reviews in the Sciences or Social Sciences and Humanities.
Main Description
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "The effort of Professor Fuller is commendable . . . [the book] provides a complete treatment of an important and frequently ignored topic. Those who work with measurement error models will find it valuable. It is the fundamental book on the subject, and statisticians will benefit from adding this book to their collection or to university or departmental libraries." -Biometrics "Given the large and diverse literature on measurement error/errors-in-variables problems, Fuller's book is most welcome. Anyone with an interest in the subject should certainly have this book." -Journal of the American Statistical Association "The author is to be commended for providing a complete presentation of a very important topic. Statisticians working with measurement error problems will benefit from adding this book to their collection." -Technometrics " . . . this book is a remarkable achievement and the product of impressive top-grade scholarly work." -Journal of Applied Econometrics Measurement Error Models offers coverage of estimation for situations where the model variables are observed subject to measurement error. Regression models are included with errors in the variables, latent variable models, and factor models. Results from several areas of application are discussed, including recent results for nonlinear models and for models with unequal variances. The estimation of true values for the fixed model, prediction of true values under the random model, model checks, and the analysis of residuals are addressed, and in addition, procedures are illustrated with data drawn from nearly twenty real data sets.
Table of Contents
List of Examplesp. xv
List of Principal Resultsp. xix
List of Figuresp. xxiii
A Single Explanatory Variablep. 1
Introductionp. 1
Ordinary Least Squares and Measurement Errorp. 1
Estimation with Known Reliability Ratiop. 5
Identificationp. 9
Measurement Variance Knownp. 13
Introduction and Estimatorsp. 13
Sampling Properties of the Estimatorsp. 15
Estimation of True x Valuesp. 20
Model Checksp. 25
Ratio of Measurement Variances Knownp. 30
Introductionp. 30
Method of Moments Estimatorsp. 30
Least Squares Estimationp. 36
Tests of Hypotheses for the Slopep. 44
Instrumental Variable Estimationp. 50
Factor Analysisp. 59
Other Methods and Modelsp. 72
Distributional Knowledgep. 72
The Method of Groupingp. 73
Measurement Error and Predictionp. 74
Fixed Observed Xp. 79
Large Sample Approximationsp. 85
Moments of the Normal Distributionp. 88
Central Limit Theorems for Sample Momentsp. 89
Notes on Notationp. 95
Vector Explanatory Variablesp. 100
Bounds for Coefficientsp. 100
The Model with an Error in the Equationp. 103
Estimation of Slope Parametersp. 103
Estimation of True Valuesp. 113
Higher-Order Approximations for Residuals and True Valuesp. 118
The Model with No Error in the Equationp. 124
The Functional Modelp. 124
The Structural Modelp. 139
Higher-Order Approximations for Residuals and True Valuesp. 140
Instrumental Variable Estimationp. 148
Modifications to Improve Moment Propertiesp. 163
An Error in the Equationp. 164
No Error in the Equationp. 173
Calibrationp. 177
Language Evaluation Datap. 181
Extensions of the Single Relation Modelp. 185
Nonnormal Errors and Unequal Error Variancesp. 185
Introduction and Estimatorsp. 186
Models with an Error in the Equationp. 193
Reliability Ratios Knownp. 199
Error Variance Functionally Related to Observationsp. 202
The Quadratic Modelp. 212
Maximum Likelihood Estimation for Known Error Covariance Matricesp. 217
Nonlinear Models with No Error in the Equationp. 225
Introductionp. 225
Models Linear in xp. 226
Models Nonlinear in xp. 229
Modifications of the Maximum Likelihood Estimatorp. 247
The Nonlinear Model with an Error in the Equationp. 261
The Structural Modelp. 261
General Explanatory Variablesp. 263
Measurement Error Correlated with True Valuep. 271
Introduction and Estimatorsp. 271
Measurement Error Models for Multinomial Random Variablesp. 272
Data for Examplesp. 281
Multivariate Modelsp. 292
The Classical Multivariate Modelp. 292
Maximum Likelihood Estimationp. 292
Properties of Estimatorsp. 303
Least Squares Estimation of the Parameters of a Covariance Matrixp. 321
Least Squares Estimationp. 321
Relationships between Least Squares and Maximum Likelihoodp. 333
Least Squares Estimation for the Multivariate Functional Modelp. 338
Factor Analysisp. 350
Introduction and Modelp. 350
Maximum Likelihood Estimationp. 353
Limiting Distribution of Factor Estimatorsp. 360
Matrix-Vector Operationsp. 382
Properties of Least Squares and Maximum Likelihood Estimatorsp. 396
Maximum Likelihood Estimation for Singular Measurement Covariancep. 404
Bibliographyp. 409
Author Indexp. 433
Subject Indexp. 435
Table of Contents provided by Ingram. All Rights Reserved.

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