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An optimal joint estimator for regression parameters and the dispersion parameter in errors-in-variables nonlinear models
Author(s):
A.
L.
Malenko;
O.
G.
Kukush
Translated by:
N. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 78
(2008).
Journal:
Theor. Probability and Math. Statist.
No. 78
(2009),
157-166.
MSC (2000):
Primary 62J02;
Secondary 62J10, 62J12, 62H12, 62F12
Posted:
August 4, 2009
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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:
-
- 1.
- R. J. Carroll, D. Ruppert, and L. A. Stefanski, Measurement Error in Nonlinear Models, Chapman and Hall, London, 1995. MR 1630517 (2000c:62001)
- 2.
- A. Kukush and H. Schneeweiss, Comparing different estimators in a nonlinear measurement error model. I, Math. Methods Statist. 14 (2005), 53-79. MR 2158071 (2006j:62068a)
- 3.
- A. Kukush and H. Schneeweiss, Asymptotic optimality of the quasi-score estimator in a class of linear score estimators, Discussion Paper, vol. 477, Universität München, SFB 386, 2006.
- 4.
- A. Kukush, A. Malenko, and H. Schneeweiss, Optimality of the quasi-score estimator in a mean-variance model with applications to measurement error models, Discussion Paper, vol. 494, Universität München, SFB 386, 2006.
- 5.
- M. J. Schervish, Theory of Statistics, Springer, New York, 1995. MR 1354146 (96m:62001)
- 6.
- S. Shklyar, H. Schneeweiss, and A. Kukush, Quasi Score is more efficient than Corrected Score in a polynomial measurement error model, Metrika 65 (2007), no. 3, 275-295. MR 2299552 (2008h:62071)
- 7.
- H. Schneeweiss, The polynomial and the Poisson measurement error models: Some further results on quasi score and corrected score estimation, Discussion Paper, vol. 446, Universität München, SFB 386, 2005.
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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:
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):
28/DEC/2006
Posted:
August 4, 2009
Dedicated:
Dedicated to our teachers, AnatoliĭYakovych Dorogovtsev and Mikhaĭlo Iosypovych Yadrenko
Copyright of article:
Copyright
2009,
American Mathematical Society
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