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Theory of Probability and Mathematical Statistics

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Consistency of the orthogonal regression estimator in an implicit linear model with errors in variables


Authors: O. O. Dashkov and A. G. Kukush
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
Journal: Theor. Probability and Math. Statist. 97 (2018), 45-55
MSC (2010): Primary 62J05; Secondary 62H12, 65F20
DOI: https://doi.org/10.1090/tpms/1047
Published electronically: February 21, 2019
MathSciNet review: 3745998
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Abstract: An implicit linear regression model with errors in variables is studied for which the true points belong to a certain hyperplane in Euclidean space and the joint covariance matrix of errors is proportional to the unit matrix. The orthogonal regression estimator for this hyperplane is considered. Some sufficient conditions for the consistency as well as for the strong consistency are given. Some applications to the explicit multiple regression model with a free term and errors in variables are shown.


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Additional Information

O. O. Dashkov
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: oodashkov@gmail.com

A. G. Kukush
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: alexander_kukush@univ.kiev.ua

DOI: https://doi.org/10.1090/tpms/1047
Keywords: Consistency of an estimator, multiple regression model with errors in variables, implicit linear regression model, orthogonal regression model, total least squares estimator
Received by editor(s): October 4, 2017
Published electronically: February 21, 2019
Article copyright: © Copyright 2019 American Mathematical Society