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Theory of Probability and Mathematical Statistics

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Conditions for the consistency of the total least squares estimator in an errors-in-variables linear regression model


Author: S. V. Shklyar
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal: Theor. Probability and Math. Statist. 83 (2011), 175-190
MSC (2010): Primary 62H12, 62J05; Secondary 62F10, 62F12, 62J10
DOI: https://doi.org/10.1090/S0094-9000-2012-00850-8
Published electronically: February 2, 2012
MathSciNet review: 2768857
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Abstract | References | Similar Articles | Additional Information

Abstract: A homoscedastic errors-in-variables linear regression model is considered. The total least squares estimator is studied. New conditions for the consistency and strong consistency of the total least squares estimator are proposed. These conditions are weaker than those proposed by Kukush and Van Huffel (Metrika 59 (2004), 75-97).


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Additional Information

S. V. Shklyar
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: shklyar@mail.univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2012-00850-8
Keywords: Linear regression, errors in variables, total least squares estimator, orthogonal regression
Received by editor(s): November 8, 2010
Published electronically: February 2, 2012
Article copyright: © Copyright 2012 American Mathematical Society