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Theory of Probability and Mathematical Statistics

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Estimation of parameters of a mixture of two symmetric distributions from a biased sample


Author: T. Gorbach
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
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
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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.


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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

DOI: https://doi.org/10.1090/tpms/949
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