Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

Request Permissions   Purchase Content 


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
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.

References [Enhancements On Off] (What's this?)

  • 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, 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, 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, Veroyatnost, “Nauka”, Moscow, 1980 (Russian). MR 609521

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 62J12

Retrieve articles in all journals with MSC (2010): 62J12

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}

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