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An adaptive moment estimator of a parameter of a distribution constructed from observations with admixture
Author(s):
N.
Lodatko;
R.
Maiboroda
Translated by:
S. Kvasko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 75
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 75
(2007),
71-82.
MSC (2000):
Primary 62G07;
Secondary 62G20
Posted:
January 24, 2008
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Additional information
Abstract:
We consider the problem of estimating an unknown parameter from observations with an admixture. The concentration of the admixture is varying with observations and assumed to be known, while its distribution is unknown. We study moment estimators and prove that they are consistent and asymptotically normal. We use an adaptive technique that allows us to determine estimators whose asymptotic variance is minimal among moment estimators.
References:
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Additional Information:
N.
Lodatko
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:
lodatko@yandex.ru
R.
Maiboroda
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:
mre@univ.kiev.ua
DOI:
10.1090/S0094-9000-08-00715-1
PII:
S 0094-9000(08)00715-1
Keywords:
Method of moments,
adaptive estimator,
a mixture with varying concentrations,
consistency,
asymptotic normality,
asymptotic variance
Received by editor(s):
19/SEP/2005
Posted:
January 24, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
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