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The uniqueness of the quasi-likelihood estimator in the Poisson model with an error in the regressor

Author: S. V. Shklyar
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 88 (2013).
Journal: Theor. Probability and Math. Statist. 88 (2014), 203-216
MSC (2010): Primary 62J12; Secondary 62H10
Published electronically: July 24, 2014
MathSciNet review: 3112645
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Abstract: The Poisson regression Berkson type model with a Gaussian error in the regressor is studied. Simple score and quasi-likelihood estimators of the regression parameters are considered. Sufficient conditions for the strong consistency of the estimators and sufficient conditions for the uniqueness of a solution of estimating equations are found. The proof of the uniqueness does not require that the parameter set be bounded.

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  • 1. Raymond J. Carroll, David Ruppert, Leonard A. Stefanski, and Ciprian M. Crainiceanu, Measurement error in nonlinear models, 2nd ed., Monographs on Statistics and Applied Probability, vol. 105, Chapman & Hall/CRC, Boca Raton, FL, 2006. A modern perspective. MR 2243417
  • 2. Alexander Kukush, Hans Schneeweis, and Roland Wolf, Three estimators for the Poisson regression model with measurement errors, Statist. Papers 45 (2004), no. 3, 351–368. MR 2064718,
  • 3. A. Kukush and H. Schneeweiss, Comparing different estimators in a nonlinear measurement error model. I, Math. Methods Statist. 14 (2005), no. 1, 53–79. MR 2158071
  • 4. R. Tyrrell Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970. MR 0274683
  • 5. H. Schneeweiss, The polynomial and the Poisson measurement error models: some further results on quasi score and corrected score estimation, SFB 386, Discussion Paper 446, LMU Munich, 2005.
  • 6. S. V. Shklyar, Asymptotic properties of estimators of parameters of nonlinear errors-in-variables regression models, Candidate Dissertation, Kyiv National Taras Shevchenko University, Kyiv, 2008. (Ukrainian)
  • 7. Markus Thamerus, Different nonlinear regression models with incorrectly observed covariates, Econometrics in theory and practice, Physica, Heidelberg, 1998, pp. 31–44. MR 1655411
  • 8. R. W. M. Wedderburn, Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method, Biometrika 61 (1974), 439–447. MR 0375592

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Additional Information

S. V. Shklyar
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine

Keywords: Regression errors-in-variables model, Poisson regression, Berkson type model
Received by editor(s): October 12, 2012
Published electronically: July 24, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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