Theory of Probability and Mathematical Statistics

Consistency of an estimator of the parameters of a polynomial regression with a known variance relation for errors in the measurement of the regressor and the echo

Author(s): S. V. Shklyar
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 76 (2007).
Journal: Theor. Probability and Math. Statist. No. 76 (2008), 181-197.
MSC (2000): Primary 62J02; Secondary 62F10, 62F12, 62J10
Posted: July 17, 2008
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Abstract: We consider an error-in-variables model for a polynomial regression with Gaussian errors. We assume that the covariance matrix of the measurement errors of the regressor and the echo is known up to a scalar factor. We consider the moment estimator of regression coefficients proposed by Cheng and Schneeweiss. Sufficient conditions for the strong consistency of this estimator are given and the rate of convergence is estimated in this paper.

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Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 62J02, 62F10, 62F12, 62J10

S. V. Shklyar
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: shklyar@mail.univ.kiev.ua

DOI: 10.1090/S0094-9000-08-00742-4
PII: S 0094-9000(08)00742-4
Keywords: Polynomial regression, error-in-variables model
Received by editor(s): 24/FEB/2006
Posted: July 17, 2008
Copyright of article: Copyright 2008, American Mathematical Society

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ISSN: 1547-7363(e) 0094-9000(p)

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