We discuss some methods of estimation in bivariate errors-in-variables linear models. We also suggest a method of constructing consistent estimators in the case when the error disturbances have the normal distribution with unknown parameters. It is based on the theory of estimating variance components in linear models. A simulation study is presented which compares this estimator with the maximum likelihood one.
@article{bwmeta1.element.bwnjournal-article-zmv25i4p401bwm, author = {Anna Czapkiewicz}, title = {On estimation of parameters in the bivariate linear errors-in-variables model}, journal = {Applicationes Mathematicae}, volume = {26}, year = {1999}, pages = {401-410}, zbl = {0992.62061}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i4p401bwm} }
Czapkiewicz, Anna. On estimation of parameters in the bivariate linear errors-in-variables model. Applicationes Mathematicae, Tome 26 (1999) pp. 401-410. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i4p401bwm/
[000] O. Bunke and H. Bunke (1989), Non-Linear Regression, Functional Relationships, and Robust Methods, Wiley, New York. | Zbl 0697.62051
[001] C. G. Chow (1983), Econometrics, Mc-Graw-Hill, New York.
[002] W. G. Cochran (1968), Errors of measurement in statistics, Technometrics 10, 637-666. | Zbl 0177.46503
[003] N. R. Cox (1976), The linear structural relation for several groups of data, Biometrika 63, 231-237. | Zbl 0338.62043
[004] W. A. Fuller (1987), Measurement Error Models, Wiley, New York. | Zbl 0800.62413
[005] L. J. Gleser, R. J. Carroll and P. P. Gallo (1987), The limiting distribution of least squares in an errors-in-variables regression model, Ann. Statist. 15, 220-233. | Zbl 0623.62015
[006] S. Gnot (1991), Estimation of Variance Components in Linear Models, Wyd. Naukowo-Techniczne, Warszawa (in Polish). | Zbl 0567.62057
[007] M. G. Kendall and A. Stuart (1979), The Advanced Theory of Statistics, Vol. 2, Griffin, London. | Zbl 0416.62001
[008] R. Kettelapper (1983), On estimating parameters in a simple error-in-variables model, Technometrics 25, 43-47.
[009] A. Olsen, J. Seely and D. Birkes (1976), Invariant quadratic unbiased estimation for two variance components, Ann. Statist. 4, 878-890. | Zbl 0344.62060
[010] S. Penev and T. Raykov (1993), On choosing estimators in a simple linear errors-in-variables model, Comm. Statist. Theory Methods 22, 2429-2444. | Zbl 0800.62135
[011] C. R. Rao (1973), Linear Statistical Inference and its Applications, Wiley, New York. | Zbl 0256.62002
[012] C. R. Rao and J. Kleffe (1988), Estimation of Variance Components and Applications, North-Holland Ser. Statist. Probab. 3, North-Holland, Amsterdam. | Zbl 0645.62073
[013] O. Reiersol (1950), Identifiability of a linear relation between variables which are subject to error, Econometrica 18, 575-589.