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Convergence of estimators in the polynomial measurement error model


Authors: A. G. Kukush and Ya. V. Tsaregorodtsev
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 92 (2015).
Journal: Theor. Probability and Math. Statist. 92 (2016), 81-91
MSC (2010): Primary 62F12, 62J02
DOI: https://doi.org/10.1090/tpms/984
Published electronically: August 10, 2016
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Abstract: A polynomial measurement error model is considered. The variance of errors in the regressor variable and the covariance between errors in the regressor variable and errors of the response variable are assumed to be known. The adjusted least squares estimator of regression parameters adopts the ordinary least squares estimator to the errors presented in the regressor. Conditions for the strong consistency of the estimator are found. These conditions are weaker as compared to those by Cheng and Schneeweiss (1998) [Journal of the Royal Statistical Society B, no. 1, 189-199]. Sufficient conditions for the asymptotic normality of the estimator are also found.


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Additional Information

A. G. Kukush
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: alexander_kukush@univ.kiev.ua

Ya. V. Tsaregorodtsev
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: 777Tsar777@mail.ru

DOI: https://doi.org/10.1090/tpms/984
Keywords: Asymptotic normality, adjusted least squares estimator, consistency of estimators, measurement error model, modification of estimators for small samples, polynomial regression
Received by editor(s): December 23, 2014
Published electronically: August 10, 2016
Article copyright: © Copyright 2016 American Mathematical Society