Estimation of mean positions and concentrations from observations of a two-component mixture of symmetric distributions
Author:
R. Maĭboroda
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 78 (2009), 147-156
MSC (2000):
Primary 62G07; Secondary 62G20
DOI:
https://doi.org/10.1090/S0094-9000-09-00768-6
Published electronically:
August 4, 2009
MathSciNet review:
2446855
Full-text PDF Free Access
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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.
References
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References
- A. A. Borovkov, Mathematical Statistics, Nauka, Moscow, 1984; English. transl., Gordon and Breach, Amsterdam, 1998. MR 782295 (86i:62001); MR 1712750 (2000f:62003)
- L. Bordes, S. Mottelet, and P. Vandekerkhove, Semiparametric estimation of a two-component mixture model, Ann. Statist. 34 (2006), no. 3, 1204–1232. MR 2278356 (2008e:62064)
- P. Hall and X.-H. Zhou, Nonparametric estimation of component distributions in a multivariate mixture, Ann. Statist. 31 (2003), no. 1, 201–224. MR 1962504 (2003m:62105)
- D. R. Hunter, S. Wang, and T. R. Hettmansperger, Inference for Mixtures of Symmetric Distributions, Technical Report 04-01, Penn State University, Philadelphia, 2004.
- G. J. McLachlan and D. Peel, Finite Mixture Models, Wiley, New York, 2000. MR 1789474 (2002b:62025)
- S. Newcomb, A generalized theory of the combination of observations so as to obtain the best result, Amer. J. Math. 8 (1886), 343–366. MR 1505430
- K. Pearson, Contributions to the mathematical theory of evolution, Phil. Trans. R. Soc. Lond. A 185 (1894), 71–110.
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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
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
