Inconsistency of the orthogonal regression estimator for the vector nonlinear errors-in-variables model
Author:
G. S. Repetats’ka
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 73 (2006), 163-179
MSC (2000):
Primary 62J02; Secondary 62F12, 62H12
DOI:
https://doi.org/10.1090/S0094-9000-07-00690-4
Published electronically:
January 17, 2007
MathSciNet review:
2213850
Full-text PDF Free Access
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Abstract: We prove that the orthogonal regression estimator for the vector errors-in-variables model is inconsistent and study its asymptotic deviation from the true value of the parameter. We also propose another estimator whose deviation from the true value is smaller than that for the orthogonal regression estimator.
References
- Wayne A. Fuller, Measurement error models, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1987. MR 898653
- Kirk M. Wolter and Wayne A. Fuller, Estimation of nonlinear errors-in-variables models, Ann. Statist. 10 (1982), no. 2, 539–548. MR 653528
- I. Fazekas, A. G. Kukush, and S. Zwanzig, On Inconsistency of the Least Squares Estimator in Nonlinear Functional Relations, Preprint, vol. 1, Department of Statistics and Demography, Odense University, Denmark, 1998.
- I. Fazekas, A. Kukush, and S. Zwanzig, Correction of nonlinear orthogonal regression estimator, Ukraïn. Mat. Zh. 56 (2004), no. 8, 1101–1118 (English, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 56 (2004), no. 8, 1308–1330. MR 2136312, DOI https://doi.org/10.1007/s11253-005-0059-0
References
- W. A. Fuller, Measurement Errors Models, Wiley, New York, 1987. MR 898653 (89a:62160)
- K. M. Wolter and W. A. Fuller, Estimation of nonlinear errors-in-variables models, Ann. Statist. 10 (1982), no. 2, 539–548. MR 653528 (83j:62099)
- I. Fazekas, A. G. Kukush, and S. Zwanzig, On Inconsistency of the Least Squares Estimator in Nonlinear Functional Relations, Preprint, vol. 1, Department of Statistics and Demography, Odense University, Denmark, 1998.
- ---, Bias correction of nonlinear orthogonal regression, Ukrain. Mat. Zh. 56 (2004), no. 8, 1101–1118. MR 2136312 (2006g:62065)
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Additional Information
G. S. Repetats’ka
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kiev 03127, Ukraine
Email:
galchonok@univ.kiev.ua
Keywords:
Orthogonal regression estimators,
nonlinear errors-in-variables model
Received by editor(s):
September 17, 2004
Published electronically:
January 17, 2007
Article copyright:
© Copyright 2007
American Mathematical Society