Abstract
We propose an easy to derive and simple to compute approximate least squares or maximum likelihood estimator for nonlinear errors-in-variables models that does not require the knowledge of the conditional density of the latent variables given the observables. Specific examples and Monte Carlo studies demonstrate that the bias of this approximate estimator is small even when the magnitude of the variance of measurement errors to the variance of measured covariates is large.
Similar content being viewed by others
References
Amemiya, T. (1985).Advanced Econometrics. Harvard University Press.
Amemiya, Y. (1985). Instrumental variable estimator for the nonlinear errors-in-variables model.Journal of Econometrics, 28, 273–290.
Amemiya, Y. and W.A. Fuller (1988). Estimation for the Nonlinear Functional Relationship.Annals of Statistics, 16, 147–160.
Berkson, J. (1950). Are There Two Regressions?Journal of the American Statistical Association, 45, 164–180.
Carroll, R.J. (1989). Covariance Analysis in Generalized Linear Measurement Error Models.Statistics in Medicine, 8, 1075–1093.
Carroll, R.J. and L.A. Stefanski (1990). Approximate Quasilikelihood Estimation in Models with Surrogate Predictors.Journal of the American Statistical Association, 85, 652–663.
Chesher, A. (1991). The Effects of Measurement Error.Biometrika, 78, 451–462.
Gleser, L.J. (1989). Improvement of the Naive Approach to Estimation in Nonlinear Errors-in-Variables Regrssion Models. Reprint.
Hsiao, C. (1989). Consistent Estimation for Some Nonlinear Errorsin-Variables Models.Journal of Econometrics, 41, 159–185.
Hsiao, C. (1991). Identification and Estimation of Dichotomous Latent Variables Models Using Panel Data.Review of Economic Studies, 58, 717–731.
Lee, L.F. and J.H. Sepanski (1995). Estimation of Linear and Nonlinear Errors-in-Variables Models Using Validation Data.Journal of the American Statistical Association, 90, 130–140.
Rosner, B., Willett, W.C. and Spiegelman D. (1989). Correction of Logistic Regression Relative Risk Estimates and Confidence Intervals for Systematic Within-Person Measurement Error.Statistics in Medicine, 8, 1051–1070.
Rudemo, M., D. Ruppert and J.C. Streibig (1989). Random Effect Models in Nonlinear Regression with Applications to Bioassay.Biometrics, 45, 349–362.
Shafer, D. (1987). Covariate Measurement Error in Generalized Linear Models.Biometrika, 74, 385–391.
Stefanski, L.A. (1985). The Effects of Measurement Error on Parameter Estimation.Biometrika, 72, 583–592.
Stefanski, L.A. and R.J. Carroll (1985). Covariate Measurement Error in Logistic Regression.Annals of Statistics, 13, 1335–1351.
Tosteson, T., Stefanski, L.A. and Schafter, D.W. (1989). A Measurement Error Model for Binary and Ordinal Regression,Statistics in Medicine, 8, 1139–1147.
Whittemore, A.S. and J.B. Keller (1988). Approximations for Regression With Covariate Measurement Error.Journal of American Statistical Association, 83, 1057–1066.
Wolter, K.M. and W.A. Fuller (1982a). Estimation of Nonlinear Errors-in-Variables Models.Annals of Statistics, 10, 539–548.
Wolter, K.M. and W.A. Fuller (1982b). Estimation of the quadratic errors-in-variables models.Biometrika, 69, 175–182.
Author information
Authors and Affiliations
Additional information
Cheng Hsiao and Qing Wang's work was supported in part by National Science Foundation grant SeS91-22481 and SBR94-09540. Liqun Wang gratefully acknowledges the financial support from Swiss National Science Foundation. We wish to thank Professor H. Schneeweiss and a referee for helpful comments and suggestions.
Rights and permissions
About this article
Cite this article
Hsiao, C., Wang, L. & Wang, Q. Estimation of nonlinear errors-in-variables models: an approximate solution. Statistical Papers 38, 1–25 (1997). https://doi.org/10.1007/BF02925212
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02925212