On estimation of parameters in the bivariate linear errors-in-variables model

Anna Czapkiewicz

Applicationes Mathematicae (1999)

  • Volume: 25, Issue: 4, page 401-410
  • ISSN: 1233-7234

Abstract

top
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.

How to cite

top

Czapkiewicz, Anna. "On estimation of parameters in the bivariate linear errors-in-variables model." Applicationes Mathematicae 25.4 (1999): 401-410. <http://eudml.org/doc/219214>.

@article{Czapkiewicz1999,
abstract = {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.},
author = {Czapkiewicz, Anna},
journal = {Applicationes Mathematicae},
keywords = {regression line; variance component; simulation study; maximum likelihood method; estimator; replication model; variance components; maximum likelihood estimators; simulations},
language = {eng},
number = {4},
pages = {401-410},
title = {On estimation of parameters in the bivariate linear errors-in-variables model},
url = {http://eudml.org/doc/219214},
volume = {25},
year = {1999},
}

TY - JOUR
AU - Czapkiewicz, Anna
TI - On estimation of parameters in the bivariate linear errors-in-variables model
JO - Applicationes Mathematicae
PY - 1999
VL - 25
IS - 4
SP - 401
EP - 410
AB - 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.
LA - eng
KW - regression line; variance component; simulation study; maximum likelihood method; estimator; replication model; variance components; maximum likelihood estimators; simulations
UR - http://eudml.org/doc/219214
ER -

References

top
  1. O. Bunke and H. Bunke (1989), Non-Linear Regression, Functional Relationships, and Robust Methods, Wiley, New York. Zbl0697.62051
  2. C. G. Chow (1983), Econometrics, Mc-Graw-Hill, New York. 
  3. W. G. Cochran (1968), Errors of measurement in statistics, Technometrics 10, 637-666. Zbl0177.46503
  4. N. R. Cox (1976), The linear structural relation for several groups of data, Biometrika 63, 231-237. Zbl0338.62043
  5. W. A. Fuller (1987), Measurement Error Models, Wiley, New York. Zbl0800.62413
  6. 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. Zbl0623.62015
  7. S. Gnot (1991), Estimation of Variance Components in Linear Models, Wyd. Naukowo-Techniczne, Warszawa (in Polish). Zbl0567.62057
  8. M. G. Kendall and A. Stuart (1979), The Advanced Theory of Statistics, Vol. 2, Griffin, London. Zbl0416.62001
  9. R. Kettelapper (1983), On estimating parameters in a simple error-in-variables model, Technometrics 25, 43-47. 
  10. A. Olsen, J. Seely and D. Birkes (1976), Invariant quadratic unbiased estimation for two variance components, Ann. Statist. 4, 878-890. Zbl0344.62060
  11. S. Penev and T. Raykov (1993), On choosing estimators in a simple linear errors-in-variables model, Comm. Statist. Theory Methods 22, 2429-2444. Zbl0800.62135
  12. C. R. Rao (1973), Linear Statistical Inference and its Applications, Wiley, New York. Zbl0256.62002
  13. C. R. Rao and J. Kleffe (1988), Estimation of Variance Components and Applications, North-Holland Ser. Statist. Probab. 3, North-Holland, Amsterdam. Zbl0645.62073
  14. O. Reiersol (1950), Identifiability of a linear relation between variables which are subject to error, Econometrica 18, 575-589. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.