Theory of Probability and Mathematical Statistics
Estimation of parameters of a mixture of two symmetric distributions from a biased sample
T. Gorbach
Download PDF
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.
Keywords: Biased sample, mixture of two symmetric distributions, generalized estimating equations, adaptive estimators
Bibliography: 1. D. M. Titterington, A. F. M. Smith, and U. E. Makov, Statistical Analysis of Finite Mixture Distribution, Wiley, New York, 1985.
2. G. J. McLachlan and D. Peel, Finite Mixture Models, Wiley-Interscience, 2000.
3. 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.
4. 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.
5. O. Sugakova, Adaptive estimators for parameters of a mixture of two symmetric distributions, Teor. Imovir. Matem. Statist. 82 (2010), 146-155; English transl. in Theor. Probability and Math. Statist. 82 (2011), 149-159.
6. D. R. Hunter, S. Wang, and T. R. Hettmansperger, Inference for mixtures of symmetric distributions, Ann. Statist. 35 (2007), 224-251.
7. J. Shao, Mathematical Statistics, Springer-Verlag, New York, 1998.
8. S. L. Lohr, Sampling: Design and Analysis, Duxbury Press, 1999.
9. O. I. Vasylyk and T. O. Yakovenko, Lectures in the Theory of Sampling Methods, Kyiv University Press, Kyiv, 2010. (Ukrainian)
10. M. V. Kartashov, Probability, Processes, Statistics, Kyiv University Press, Kyiv, 2007. (Ukrainian)
