Electronic ISBN:  9780821877005 
Product Code:  CONM/112.E 
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Book DetailsContemporary MathematicsVolume: 112; 1990; 248 ppMSC: Primary 62;
Measurement error models describe functional relationships among variables observed, subject to random errors of measurement. Examples include linear and nonlinear errorsinvariables 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 AMSIMSSIAM 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 [ MR 1087094 ]

Peter Sprent  Some history of functional and structural relationships [ MR 1087095 ]

Alice S. Whittemore  Errorsinvariables regression problems in epidemiology [ MR 1087096 ]

Hans Schneeweiss  Models with latent variables: LISREL versus PLS [ MR 1087097 ]

Wayne A. Fuller  Prediction of true values for the measurement error model [ MR 1087098 ]

Stephen M. Miller  Analysis of residuals from measurement error models [ MR 1087099 ]

John L. Eltinge  Errorsinvariables estimation in the presence of serially correlated observations [ MR 1087100 ]

Nonlinear Models [ MR 1087094 ]

Leon Jay Gleser  Improvements of the naive approach to estimation in nonlinear errorsinvariables regression models [ MR 1087101 ]

Leonard A. Stefanski and Raymond J. Carroll  Structural logistic regression measurement error models [ MR 1087102 ]

Daniel W. Schafer  Measurement error model estimation using iteratively weighted least squares [ MR 1087103 ]

Philip J. Brown and Samuel D. Oman  Problematic points in nonlinear calibration [ MR 1087104 ]

Yasuo Amemiya  Instrumental variable estimation of the nonlinear measurement error model [ MR 1087105 ]

Daniel J. Schnell  A likelihood ratio test for error covariance specification in nonlinear measurement error models [ MR 1087106 ]

Cliff H. Spiegelman  Plotting techniques for errorsinvariables problems [ MR 1087107 ]

Computational Aspects [ MR 1087094 ]

G. W. Stewart  Perturbation theory and least squares with errors in the variables [ MR 1087108 ]

Paul T. Boggs and Janet E. Rogers  Orthogonal distance regression [ MR 1087109 ]

Nicholas J. Higham  Computing error bounds for regression problems [ MR 1087110 ]

Robust Procedures [ MR 1087094 ]

M. W. Browne  Asymptotic robustness of normal theory methods for the analysis of latent curves [ MR 1087111 ]

Chi Lun Cheng and John W. Van Ness  Bounded influence errorsinvariables regression [ MR 1087112 ]

Víctor J. Yohai and Ruben H. Zamar  Bounded influence estimation in the errorsinvariables model [ MR 1087113 ]


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Measurement error models describe functional relationships among variables observed, subject to random errors of measurement. Examples include linear and nonlinear errorsinvariables 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 AMSIMSSIAM 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.

General Problems [ MR 1087094 ]

Peter Sprent  Some history of functional and structural relationships [ MR 1087095 ]

Alice S. Whittemore  Errorsinvariables regression problems in epidemiology [ MR 1087096 ]

Hans Schneeweiss  Models with latent variables: LISREL versus PLS [ MR 1087097 ]

Wayne A. Fuller  Prediction of true values for the measurement error model [ MR 1087098 ]

Stephen M. Miller  Analysis of residuals from measurement error models [ MR 1087099 ]

John L. Eltinge  Errorsinvariables estimation in the presence of serially correlated observations [ MR 1087100 ]

Nonlinear Models [ MR 1087094 ]

Leon Jay Gleser  Improvements of the naive approach to estimation in nonlinear errorsinvariables regression models [ MR 1087101 ]

Leonard A. Stefanski and Raymond J. Carroll  Structural logistic regression measurement error models [ MR 1087102 ]

Daniel W. Schafer  Measurement error model estimation using iteratively weighted least squares [ MR 1087103 ]

Philip J. Brown and Samuel D. Oman  Problematic points in nonlinear calibration [ MR 1087104 ]

Yasuo Amemiya  Instrumental variable estimation of the nonlinear measurement error model [ MR 1087105 ]

Daniel J. Schnell  A likelihood ratio test for error covariance specification in nonlinear measurement error models [ MR 1087106 ]

Cliff H. Spiegelman  Plotting techniques for errorsinvariables problems [ MR 1087107 ]

Computational Aspects [ MR 1087094 ]

G. W. Stewart  Perturbation theory and least squares with errors in the variables [ MR 1087108 ]

Paul T. Boggs and Janet E. Rogers  Orthogonal distance regression [ MR 1087109 ]

Nicholas J. Higham  Computing error bounds for regression problems [ MR 1087110 ]

Robust Procedures [ MR 1087094 ]

M. W. Browne  Asymptotic robustness of normal theory methods for the analysis of latent curves [ MR 1087111 ]

Chi Lun Cheng and John W. Van Ness  Bounded influence errorsinvariables regression [ MR 1087112 ]

Víctor J. Yohai and Ruben H. Zamar  Bounded influence estimation in the errorsinvariables model [ MR 1087113 ]