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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

An optimal joint estimator for regression parameters and the dispersion parameter in errors-in-variables nonlinear models


Authors: A. L. Malenko and O. G. Kukush
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 78 (2008).
Journal: Theor. Probability and Math. Statist. 78 (2009), 157-166
MSC (2000): Primary 62J02; Secondary 62J10, 62J12, 62H12, 62F12
Published electronically: August 4, 2009
MathSciNet review: 2446856
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider an errors-in-variables nonlinear structural model where the density of the response belongs to the exponential family. We estimate regression parameters and the dispersion parameter as well as parameters of the hidden variable. Following the modified quasi-likelihood method we construct a joint estimator that has the minimal asymptotic covariance matrix in a wide class of estimators. The polynomial and gamma models are studied in more detail.


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

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Additional Information

A. L. Malenko
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: exipilis@yandex.ru

O. G. Kukush
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: alexander_kukush@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00769-8
PII: S 0094-9000(09)00769-8
Keywords: Exponential family of densities, errors-in-variables models, polynomial model, gamma model, quasi-likelihood method, asymptotic effectiveness of estimators
Received by editor(s): December 28, 2006
Published electronically: August 4, 2009
Dedicated: Dedicated to our teachers, Anatoli&ibreve;Yakovych Dorogovtsev and Mikha&ibreve;lo Iosypovych Yadrenko
Article copyright: © Copyright 2009 American Mathematical Society



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