Estimation of parameters of a mixture of two symmetric distributions from a biased sample
Author:
T. Gorbach
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 90 (2015), 57-69
MSC (2010):
Primary 62G05; Secondary 62G20
DOI:
https://doi.org/10.1090/tpms/949
Published electronically:
August 6, 2015
MathSciNet review:
3241860
Full-text PDF Free Access
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Additional Information
Abstract: We consider a biased sample from a mixture of two symmetric distributions that differ by a shift parameter. The method of moments and the generalized estimating equations method are used to estimate unknown parameters. Adaptive estimators are constructed by using the estimators of optimal estimating functions and those obtained by the method of moments. The asymptotic behavior of GEE-estimators and adaptive estimators is investigated.
References
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References
- D. M. Titterington, A. F. M. Smith, and U. E. Makov, Statistical Analysis of Finite Mixture Distribution, Wiley, New York, 1985. MR 838090 (87j:62033)
- G. J. McLachlan and D. Peel, Finite Mixture Models, Wiley-Interscience, 2000. MR 1789474 (2002b:62025)
- R. E. Maĭboroda, Estimation of mean positions and concentrations from observations of a two-component mixture of symmetric distributions, Teor. Imovir. Matem. Statist. 78 (2008), 133–141; English transl. in Theor. Probability and Math. Statist. 78 (2009), 147–156. MR 2446855 (2010b:62134)
- R. E. Maĭboroda and O. Sugakova, Estimate for Euclidean parameters of a mixture of two symmetric distributions, Ukr. Matem. Zh. 62 (2010), no. 7, 945–953; English transl. in Ukrain. Math. J. 62 (2010), no. 7, 1098–1108. MR 2888662
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- J. Shao, Mathematical Statistics, Springer-Verlag, New York, 1998. MR 2002723 (2004g:62002)
- S. L. Lohr, Sampling: Design and Analysis, Duxbury Press, 1999. MR 3057878
- O. I. Vasylyk and T. O. Yakovenko, Lectures in the Theory of Sampling Methods, Kyiv University Press, Kyiv, 2010. (Ukrainian)
- M. V. Kartashov, Probability, Processes, Statistics, Kyiv University Press, Kyiv, 2007. (Ukrainian)
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Additional Information
T. Gorbach
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine
Keywords:
Biased sample,
mixture of two symmetric distributions,
generalized estimating equations,
adaptive estimators
Received by editor(s):
July 31, 2013
Published electronically:
August 6, 2015
Article copyright:
© Copyright 2015
American Mathematical Society
