Adaptive estimators for parameters of a mixture of two symmetric distributions
Author:
O. Sugakova
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 82 (2011), 149-159
MSC (2010):
Primary 62G05; Secondary 62G20
DOI:
https://doi.org/10.1090/S0094-9000-2011-00834-4
Published electronically:
August 5, 2011
MathSciNet review:
2790490
Full-text PDF Free Access
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Abstract: A sample is observed from a mixture of two symmetric distributions that differ only by the location parameters. We use the method of estimating equations to estimate unknown parameters of the components. The methods works as follows: first, we construct an estimator for the optimal estimating functions; then we use it to construct adaptive estimators. We study the asymptotic behavior of resulting estimators.
References
- R. Maĭboroda and O. Sugakova, Estimation of Euclidean parameters of a mixture of two symmetric distributions, Ukrain. Mat. Zh. 62 (2010), 945–953. (Ukrainian)
- Laurent Bordes, Stéphane Mottelet, and Pierre Vandekerkhove, Semiparametric estimation of a two-component mixture model, Ann. Statist. 34 (2006), no. 3, 1204–1232. MR 2278356, DOI https://doi.org/10.1214/009053606000000353
- David R. Hunter, Shaoli Wang, and Thomas P. Hettmansperger, Inference for mixtures of symmetric distributions, Ann. Statist. 35 (2007), no. 1, 224–251. MR 2332275, DOI https://doi.org/10.1214/009053606000001118
- R. Maĭboroda, Estimation of mean positions and concentrations from observations of a two-component mixture of symmetric distributions, Teor. Ĭmovīr. Mat. Stat. 78 (2008), 132–140 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 78 (2009), 147–156. MR 2446855, DOI https://doi.org/10.1090/S0094-9000-09-00768-6
- Jun Shao, Mathematical statistics, 2nd ed., Springer Texts in Statistics, Springer-Verlag, New York, 2003. MR 2002723
References
- R. Maĭboroda and O. Sugakova, Estimation of Euclidean parameters of a mixture of two symmetric distributions, Ukrain. Mat. Zh. 62 (2010), 945–953. (Ukrainian)
- L. Bordes, S. Mottelet, and P. Vandekerkhove, Semiparametric estimation of a two-component mixture model, Ann. Statist. 34 (2006), 1204–1232. MR 2278356 (2008e:62064)
- D. R. Hunter, S. Wang, and T. R. Hettmansperger, Inference for mixtures of symmetric distributions, Ann. Statist. 35 (2007), 224–251. MR 2332275 (2008g:62079)
- R. Maĭboroda, Estimation of mean positions and concentrations from observations of a two-component mixture of symmetric distributions, Teor. Imovir. Mat. Stat. 78 (2008), 132–140; English transl. in Theory Probab. Math. Statist. 78 (2009), 147–156. MR 2446855 (2010b:62134)
- J. Shao, Mathematical Statistics, Springer-Verlag, New York, 1998. MR 2002723 (2004g:62002)
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Additional Information
O. Sugakova
Affiliation:
Department of Mathematics and Theoretical Radiophysics, Faculty for Radiophysics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email:
sugak@univ.kiev.ua
Keywords:
Mixture,
estimating equations,
adaptive estimators for parameters
Received by editor(s):
February 17, 2010
Published electronically:
August 5, 2011
Article copyright:
© Copyright 2011
American Mathematical Society
