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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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