The asymptotic normality of an adjusted least squares estimator in a multivariate vector errors-in-variables regression model

Author:
I. O. Sen’ko

Translated by:
N. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **88** (2013).

Journal:
Theor. Probability and Math. Statist. **88** (2014), 175-190

MSC (2010):
Primary 62J12

DOI:
https://doi.org/10.1090/S0094-9000-2014-00929-1

Published electronically:
July 24, 2014

MathSciNet review:
3112643

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An adjusted least squares estimator in a linear multivariate vector error-in-variables regression model is considered in this paper. Conditions for the asymptotic normality of this estimator are given. A modification of the estimator is constructed whose asymptotic properties are the same as those of the adjusted least squares estimator and which is stable even if a sample is small.

**1.**R. J. Carroll, D. Ruppert, and L. A. Stefanski,*Measurement error in nonlinear models*, Monographs on Statistics and Applied Probability, vol. 63, Chapman & Hall, London, 1995. MR**1630517****2.**Chi-Lun Cheng, Hans Schneeweiss, and Markus Thamerus,*A small sample estimator for a polynomial regression with errors in the variables*, J. R. Stat. Soc. Ser. B Stat. Methodol.**62**(2000), no. 4, 699–709. MR**1796286**, https://doi.org/10.1111/1467-9868.00258**3.**Wayne A. Fuller,*Measurement error models*, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1987. MR**898653****4.**Paul P. Gallo,*Consistency of regression estimates when some variables are subject to error*, Comm. Statist. A—Theory Methods**11**(1982), no. 9, 973–983. MR**655466****5.**Richard Bellman,*Introduction to matrix analysis*, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960. MR**0122820****6.**F. R. Gantmakher,*\cyr Teoriya matrits*, 4th ed., “Nauka”, Moscow, 1988 (Russian). Edited and with a foreword and an appendix by V. B. Lidskiĭ. MR**986246****7.**I. O. Sen'ko,*The consistence of an adjusted least squares estimator in a linear vector errors-in-variables model*(to appear).**8.**Valentin V. Petrov,*Limit theorems of probability theory*, Oxford Studies in Probability, vol. 4, The Clarendon Press, Oxford University Press, New York, 1995. Sequences of independent random variables; Oxford Science Publications. MR**1353441****9.**A. N. Širjaev,*\cyr Veroyatnost′*, “Nauka”, Moscow, 1980 (Russian). MR**609521**

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Additional Information

**I. O. Sen’ko**

Affiliation:
Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine

Email:
ivan{\textunderscore}senko@ukr.net

DOI:
https://doi.org/10.1090/S0094-9000-2014-00929-1

Keywords:
Error-in-variables models,
adjusted least squares estimator,
asymptotic normality,
small samples

Received by editor(s):
October 25, 2012

Published electronically:
July 24, 2014

Article copyright:
© Copyright 2014
American Mathematical Society