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Theory of Probability and Mathematical Statistics

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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
DOI: https://doi.org/10.1090/S0094-9000-2014-00928-X
Published electronically: July 24, 2014
MathSciNet review: 3112645
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Abstract | References | Similar Articles | Additional Information

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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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
Email: shklyar@mail.univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2014-00928-X
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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