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Statistical Analysis of Measurement Error Models and Applications
Edited by: Philip J. Brown and Wayne A. Fuller
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Contemporary Mathematics
1990; 248 pp; softcover
Volume: 112
ISBN-10: 0-8218-5117-9
ISBN-13: 978-0-8218-5117-3
List Price: US$67
Member Price: US$53.60
Order Code: CONM/112
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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

GENERAL PROBLEMS
  • P. Sprent -- Some history of functional and structural relationships
  • A. S. Whittemore -- Errors-in-variables regression problems in epidemiology
  • H. Schneeweiss -- Models with latent variables: LISREL versus PLS
  • W. A. Fuller -- Prediction of true values for the measurement error model
  • S. M. Miller -- Analysis of residuals from measurement error models
  • J. L. Eltinge -- Errors-in-variables estimation in the presence of serially correlated observations
NONLINEAR MODELS
  • L. J. Gleser -- Improvements of the naive approach to estimation in nonlinear errors-in-variables regression models
  • L. A. Stefanski and R. J. Carroll -- Structural logistic regression measurement error models
  • D. W. Schafer -- Measurement error model estimation using iteratively weighted least squares
  • P. J. Brown and S. D. Oman -- Problematic points in nonlinear calibration
  • Y. Amemiya -- Instrumental variable estimation of the nonlinear measurement error model
  • D. J. Schnell -- A likelihood ratio test for error covariance specification in nonlinear measurement error models
  • C. J. Spiegelman -- Plotting techniques for errors in variables problems
COMPUTATIONAL ASPECTS
  • G. W. Stewart -- Perturbation theory and least squares with errors in the variables
  • P. T. Boggs and J. E. Rogers -- Orthogonal distance regression
  • N. J. Higham -- Computing error bounds for regression problems
ROBUST PROCEDURES
  • M. W. Browne -- Asymptotic robustness of normal theory methods for the analysis of latent curves
  • C.-L. Cheng and J. W. Van Ness -- Bounded influence errors-in-variables regression
  • V. J. Yohai and R. H. Zamar -- Bounded influence estimation in the errors-in-variables model
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