Theory of Probability and Mathematical Statistics

Inconsistency of the orthogonal regression estimator for the vector nonlinear errors-in-variables model

Author(s): G. S. Repetats'ka
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 73 (2005).
Journal: Theor. Probability and Math. Statist. No. 73 (2006), 163-179.
MSC (2000): Primary 62J02; Secondary 62F12, 62H12
Posted: January 17, 2007
Retrieve article in: PDF DVI PostScript

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.

1.: W. A. Fuller, Measurement Errors Models, Wiley, New York, 1987. MR 898653 (89a:62160)
2.: 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)
3.: 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.
4.: -, Bias correction of nonlinear orthogonal regression, Ukrain. Mat. Zh. 56 (2004), no. 8, 1101-1118. MR 2136312 (2006g:62065)

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 62J02, 62F12, 62H12

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

DOI: 10.1090/S0094-9000-07-00690-4
PII: S 0094-9000(07)00690-4
Keywords: Orthogonal regression estimators, nonlinear errors-in-variables model
Received by editor(s): 17/SEP/2004
Posted: January 17, 2007
Copyright of article: Copyright 2007, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN: 1547-7363(e) 0094-9000(p)

Previous number \| Table of contents \| Next number Recently posted articles \| Most recent number \| All numbers Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS