**Contemporary Mathematics**

Volume: 112;
1990;
248 pp;
Softcover

MSC: Primary 62;

**Print ISBN: 978-0-8218-5117-3
Product Code: CONM/112**

List Price: $76.00

AMS Member Price: $60.80

MAA Member Price: $68.40

**Electronic ISBN: 978-0-8218-7700-5
Product Code: CONM/112.E**

List Price: $71.00

AMS Member Price: $56.80

MAA Member Price: $63.90

# Statistical Analysis of Measurement Error Models and Applications

Share this page *Edited by *
*Philip J. Brown; Wayne A. Fuller*

Measurement error models describe functional relationships
among variables observed, subject to random errors of
measurement. Examples include linear and nonlinear errors-in-variables
regression models, calibration and inverse regression models, factor
analysis models, latent structure models, and simultaneous equations
models. Such models are used in a wide variety of areas, including
medicine, the life sciences, econometrics, chemometrics, geology,
sample surveys, and time series. Although the problem of estimating
the parameters of such models exists in most scientific fields, there
is a need for more sources that treat measurement error models as an
area of statistical methodology. This volume is designed to address
that need.

This book contains the proceedings of an AMS-IMS-SIAM Joint Summer
Research Conference in the Mathematical Sciences on Statistical
Analysis of Measurement Error Models and Applications. The conference
was held at Humboldt State University in Arcata, California in June
1989. The papers in this volume fall into four broad groups. The first
group treats general aspects of the measurement problem and features a
discussion of the history of measurement error models. The second
group focuses on inference for the nonlinear measurement error model,
an active area of research which generated considerable interest at
the conference. The third group of papers examines computational
aspects of estimation, while the final set studies estimators
possessing robustness properties against deviations from common model
assumptions.

# Table of Contents

## Statistical Analysis of Measurement Error Models and Applications

- Contents ix10 free
- Preface xi12 free
- General Problems 114 free
- Some History of Functional and Structural Relationships 316
- Errors-in-Variables Regression Problems in Epidemiology 1730
- Models with Latent Variables: LISREL Versus PLS 3346
- Prediction of True Values for the Measurement Error Model 4154
- Analysis of Residuals from Measurement Error Models 5972
- Errors-in-Variables Estimation in the Presence of Serially Correlated Observations 7386

- Nonlinear Models 97110
- Improvements of the Naive Approach to Estimation in Nonlinear Errors-in-Variables Regression Models 99112
- Structural Logistic Regression Measurement Error Models 115128
- Measurement Error Model Estimation Using Iteratively Weighted Least Squares 129142
- Problematic Points in Nonlinear Calibration 139152
- Instrumental Variable Estimation of the Nonlinear Measurement Error Model 147160
- A Likelihood Ratio Test for Error Covariance Specification in Nonlinear Measurement Error Models 157170
- Plotting Techniques for Errors-in-Variables Problems 167180

- Computational Aspects 169182
- Robust Procedures 209222