On the Equivalence between Orthogonal Regression and Linear Model with Type-II Constraints

Sandra Donevska; Eva Fišerová; Karel Hron

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2011)

  • Volume: 50, Issue: 2, page 19-27
  • ISSN: 0231-9721

Abstract

top
Orthogonal regression, also known as the total least squares method, regression with errors-in variables or as a calibration problem, analyzes linear relationship between variables. Comparing to the standard regression, both dependent and explanatory variables account for measurement errors. Through this paper we shortly discuss the orthogonal least squares, the least squares and the maximum likelihood methods for estimation of the orthogonal regression line. We also show that all mentioned approaches lead to the same estimates in a special case.

How to cite

top

Donevska, Sandra, Fišerová, Eva, and Hron, Karel. "On the Equivalence between Orthogonal Regression and Linear Model with Type-II Constraints." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 50.2 (2011): 19-27. <http://eudml.org/doc/196302>.

@article{Donevska2011,
abstract = {Orthogonal regression, also known as the total least squares method, regression with errors-in variables or as a calibration problem, analyzes linear relationship between variables. Comparing to the standard regression, both dependent and explanatory variables account for measurement errors. Through this paper we shortly discuss the orthogonal least squares, the least squares and the maximum likelihood methods for estimation of the orthogonal regression line. We also show that all mentioned approaches lead to the same estimates in a special case.},
author = {Donevska, Sandra, Fišerová, Eva, Hron, Karel},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {linear regression model with type-II constraints; orthogonal regression; estimation; estimation},
language = {eng},
number = {2},
pages = {19-27},
publisher = {Palacký University Olomouc},
title = {On the Equivalence between Orthogonal Regression and Linear Model with Type-II Constraints},
url = {http://eudml.org/doc/196302},
volume = {50},
year = {2011},
}

TY - JOUR
AU - Donevska, Sandra
AU - Fišerová, Eva
AU - Hron, Karel
TI - On the Equivalence between Orthogonal Regression and Linear Model with Type-II Constraints
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2011
PB - Palacký University Olomouc
VL - 50
IS - 2
SP - 19
EP - 27
AB - Orthogonal regression, also known as the total least squares method, regression with errors-in variables or as a calibration problem, analyzes linear relationship between variables. Comparing to the standard regression, both dependent and explanatory variables account for measurement errors. Through this paper we shortly discuss the orthogonal least squares, the least squares and the maximum likelihood methods for estimation of the orthogonal regression line. We also show that all mentioned approaches lead to the same estimates in a special case.
LA - eng
KW - linear regression model with type-II constraints; orthogonal regression; estimation; estimation
UR - http://eudml.org/doc/196302
ER -

References

top
  1. Anděl, J., Statistical Methods, Matfyzpress, Praha, 2007, (in Czech). (2007) 
  2. Caroll, R. J., Ruppert, D., The use and misuse of orthogonal regression in linear errors-in-variables models, Am. Stat. 50 (1996), 1–6. (1996) 
  3. Casella, G., Berger, R. L., Statistical Inference, Duxbury Press, Pacific Grove, 2002, (sec. ed.). (2002) 
  4. Fišerová, E., Hron, K., 10.1080/02664760902914532, Journal of Applied Statistics 37 (2010), 1137–1152. (2010) MR2751926DOI10.1080/02664760902914532
  5. Fišerová, E., Kubáček, L., Kunderová, P., Linear Statistical Models: Regularity and Singularities, Academia, Praha, 2007. (2007) 
  6. Fuller, W. A., Measurement Error Models, Wiley, New York, 1987. (1987) Zbl0800.62413MR0898653
  7. Hillegers, L. T. M. E., The estimation of parameters in functional relationship models, Dissertation, Eindhoven University of Technology, Eindhoven, The Netherlands, 1986. (1986) MR0874750
  8. Jackson, J. D., Dunlevy, J. A., Orthogonal least squares and the interchangeability of alternative proxy variables in the social sciences, Journal of the Royal Statistical Society Series D (The Statistician) 37, 1 (1988), 7–14. (1988) 
  9. Jolicoeur, P., 10.2307/2528326, Biometrics 24 (1968), 679–682. (1968) DOI10.2307/2528326
  10. Kendall, M. G., Stuart, A., The Advanced Theory of Statistics, Vol. 2, Charles Griffin, London, 1967. (1967) 
  11. Kubáček, L., Kubáčková, L., One of the calibration problems, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 36 (1997), 117–130. (1997) MR1620541
  12. Markovsky, I., Van Huffel, S., 10.1016/j.sigpro.2007.04.004, Signal Processing 87 (2007), 2283–2320. (2007) Zbl1186.94229DOI10.1016/j.sigpro.2007.04.004
  13. Nestares, O., Fleet, D. J., Heeger, D. J., Likelihood functions and confidence bounds for total-least-squares problems, In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’00) 1 (2000), 1523–1530. (2000) 
  14. Van Huffel, S., Lemmerling, P., Total Least Squares and Errors-in-Variables Modelling: Analysis, Algorithms and Applications, Kluwer, Dordrecht, 2002. (2002) MR1951009
  15. Van Huffel, S., Vandevalle, J., The Total Least Squares Problem: Computational Aspects and Analysis, SIAM, Philadelphia, 1991. (1991) MR1118607
  16. Wimmer, G., Witkovský, V., 10.1080/10629360600679433, J. Stat. Comput. Simul. 77 (2007), 213–227. (2007) MR2345730DOI10.1080/10629360600679433

NotesEmbed ?

top

You must be logged in to post comments.