Asymptotic behavior of SIMEX estimators in an errors-in-variables linear structural regression model
Author:
O. B. Gontar
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 78 (2009), 1-13
MSC (2000):
Primary 62J05, 62F12, 62-07
DOI:
https://doi.org/10.1090/S0094-9000-09-00757-1
Published electronically:
August 4, 2009
MathSciNet review:
2446844
Full-text PDF Free Access
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Abstract: We study the SIMEX estimators in an errors-in-variables linear structural regression model. The SIMEX method was introduced by Cook and Stefanski (1994). We investigate the behavior of adjusted SIMEX estimators proposed by Polzehl and Zwanzig (2005) as the size of a sample increases. We prove that the estimators are consistent and asymptotically normal.
References
- Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
- 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
- Chi-Lun Cheng and John W. Van Ness, Statistical regression with measurement error, Kendall’s Library of Statistics, vol. 6, Arnold, London; co-published by Oxford University Press, New York, 1999. MR 1719513
- J. R. Cook and L. A. Stefanski, Simulation-extrapolation estimation in parametric measurement error models, J. Amer. Stat. Assoc. 89 (1994), 1314–1328.
- 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
- J. Polzehl and S. Zwanzig, SIMEX and TLS: An Equivalence Result, Technical Report 999, WIAS, Berlin, 2005.
References
- P. Billingsley, Convergence of Probability Measures, John Wiley, New York, 1968. MR 0233396 (38:1718)
- R. J. Carroll, D. Ruppert, and L. A. Stefanski, Measurement Error in Nonlinear Models, Chapman and Hall, London, 1996. MR 1630517 (2000c:62001)
- C.-L. Cheng and John W. Van Ness, Statistical Regression with Measurement Error, Oxford University Press, New York, 1999. MR 1719513 (2001k:62001)
- J. R. Cook and L. A. Stefanski, Simulation-extrapolation estimation in parametric measurement error models, J. Amer. Stat. Assoc. 89 (1994), 1314–1328.
- W. A. Fuller, Measurement Error Models, Wiley, New York, 1987. MR 898653 (89a:62160)
- J. Polzehl and S. Zwanzig, SIMEX and TLS: An Equivalence Result, Technical Report 999, WIAS, Berlin, 2005.
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Additional Information
O. B. Gontar
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:
gontaro@ukr.net
Keywords:
SIMEX estimators,
errors-in-variables models
Received by editor(s):
October 23, 2006
Published electronically:
August 4, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
