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