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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Estimation of mean positions and concentrations from observations of a two-component mixture of symmetric distributions


Author: R. Maĭboroda
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 78 (2008).
Journal: Theor. Probability and Math. Statist. 78 (2009), 147-156
MSC (2000): Primary 62G07; Secondary 62G20
Published electronically: August 4, 2009
MathSciNet review: 2446855
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Abstract | References | Similar Articles | Additional Information

Abstract: A statistician observes a sample from a mixture of two symmetric distributions that differ from one another by a shift parameter. Estimators for mean position parameters and concentrations (mixing probabilities) for both components are constructed by the method of moments. Conditions for the consistence and asymptotic normality of these estimators are obtained. The asymptotic variance (dispersion coefficient) of the estimator of the concentration is found.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00768-6
PII: S 0094-9000(09)00768-6
Keywords: Method of moments, a finite mixture of probability distributions, consistence, asymptotic normality, asymptotic variance
Received by editor(s): March 22, 2007
Published electronically: August 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society