Summary
In this paper it is investigated whether robust estimation procedures for the parameters of a regression model are also applicable when the observations are generated by the errors-in-variables model. Specifically, attention is paid to bounded-influence estimators, i.e. estimators that are constructed in such a way that the influence of a single observation on the outcome of the estimator is bounded. Both the classical errors-in-variables model and models with contaminated observational errors are considered.
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References
Andrews, D.F., et al.: Robust estimates of location: survey and advances. Princeton 1972.
Fuller, W.A.: Properties of some estimators for the errors-in-variables model. Annals of Statistics8, 1980, 407–422.
Hampel, F.R.: The influence curve and its role in robust estimation. Journal of the American Statistical Association 69, 1974, 383–393.
Huber, P.J.: Robust estimation of a location parameter. Annals of Math. Stat. 35, 1964, 73–101.
—: Robust regression: asymptotics, conjectures and Monte Carlo. The Annals of Statistics 1, 1973, 799–821.
Kendall, M.G., andA. Stuart: The advanced theory of statistics, vol. 2, London 1973.
Krasker, W.S.: Estimation in linear regression models with disparate data points. Econometrica 48, 1980, 1333–1346.
Krasker, W.S., andR.E. Welsch: Efficient bounded influence regression estimation using alternative definitions of sensitivity. Tech. Report MIT, 1979.
Maronna, R., O. Bustor, andV. Yohai: Bias- and efficiency- robustness of generalM-estimators for regression with random carriers. In: Smoothing Techniques for Curve Estimation. Berlin 1979.
Moran, P.A.P.: Estimating structural and functional relationships. Journal of Multivariate Analysis 1, 1971, 232–255.
Schneeweiß, H.: Consistent estimation of a regression with errors in the variables. Metrika 23, 1976, 101–115.
—: Different asymptotic variances for the same estimator in a regression with errors in the variables. Methods of Operations Research 36, 1980, 249–269.
Schneeweiß, H.: A simple regression model with trend and error in the exogenous variable. In: Games, Economic Dynamics, and Time Series Analysis. A Symposium in Memoriam Oskar Morgenstern Organized at the Institute for Advanced Studies, Vienna. Ed. by M. Deistler, E. Fürst, and G. Schwödiauer, Vienna 1982.
Wald, A.: The fitting of straight lines if both variables are subject to error. Annals of Mathematical Statistics 11, 1940, 285–300.
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The authors are indebted to a referee for his valuable comments on an earlier version of this paper.
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Ketellapper, R.H., Ronner, A.E. Are robust estimation methods useful in the structural errors-in-variables model?. Metrika 31, 33–41 (1984). https://doi.org/10.1007/BF01915180
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DOI: https://doi.org/10.1007/BF01915180