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

Full-text PDF Free Access

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

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