An adaptive moment estimator of a parameter of a distribution constructed from observations with admixture
Authors:
N. Lodatko and R. Maĭboroda
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 75 (2007), 71-82
MSC (2000):
Primary 62G07; Secondary 62G20
DOI:
https://doi.org/10.1090/S0094-9000-08-00715-1
Published electronically:
January 24, 2008
MathSciNet review:
2321182
Full-text PDF Free Access
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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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References
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- O. O. Kubaychuk, Estimation of moments from mixtures with the use of improved weighted empirical distribution function, Visnyk Kyiv Univ. Matematyka. Mekhanika 9–10 (2003), 48–52 . (Ukrainian)
- O. O. Kubaychuk, Statistical analysis of characteristics of random variables with the use of observations of a mixture, Ph.D. Dissertation, Kyiv National University, Kyiv, 2004. (Ukrainian)
- A. Lodatko and R. Maĭboroda, Estimation of the probability density by observations with an admixture, Teor. Imovir. Mat. Stat. 73 (2005), 88–96; English transl. in Theory Probab. Math. Statist. 73 (2006), 99–108. MR 2213844 (2007b:62043)
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- C. Stone, Adaptive maximum likelihood estimation of a location parameter, Ann. Statist. 3 (1975), 267–284. MR 0362669 (50:15109)
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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. Maĭboroda
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
Keywords:
Method of moments,
adaptive estimator,
a mixture with varying concentrations,
consistency,
asymptotic normality,
asymptotic variance
Received by editor(s):
September 19, 2005
Published electronically:
January 24, 2008
Article copyright:
© Copyright 2008
American Mathematical Society
