Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

Request Permissions   Purchase Content 
 
 

 

Lower bound for a dispersion matrix for the semiparametric estimation in a model of mixtures


Author: O. V. Doronin
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
Journal: Theor. Probability and Math. Statist. 90 (2015), 71-85
MSC (2010): Primary 62G05, 62G20, 62F12; Secondary 62P25, 62G30
DOI: https://doi.org/10.1090/tpms/950
Published electronically: August 6, 2015
MathSciNet review: 3241861
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The model of mixtures with varying concentrations is discussed. The parameterization of the first $ K$ of $ M$ components is considered. The semiparametric estimation technique based on the method of generalized estimating equations is considered. The consistency and asymptotic normality of estimators are proved. A lower bound for the dispersion matrix is found.


References [Enhancements On Off] (What's this?)

  • 1. A. A. Borovkov, Mathematical Statistics, ``Nauka'', Moscow, 1984; English transl., Gordon and Breach Science Publishers, Amsterdam, 1998. (Translated from the Russian by A. Moullagaliev and revised by the author) MR 1712750 (2000f:62003)
  • 2. O. V. Doronin, Robust estimates for mixtures with a Gaussian component, Visnyk Kyiv National Taras Shevchenko University. Mathematics and Mechanics (2012), no. 1, 18-23. (Ukrainian)
  • 3. N. Lodatko and R. Maĭboroda, An adaptive moment estimator of a parameter of a distribution constructed from observations with admixture, Teor. Imovirnost. Matem. Statist. 75 (2006), 61-70; English transl in Theor. Probability and Math. Statist. 75 (2007), 71-82. MR 2321182 (2008g:62101)
  • 4. R. E. Maiboroda and O. V. Sugakova, An estimation and classification by observations from a mixture, Kyiv University Press, Kyiv, 2008. (Ukrainian)
  • 5. D. I. Pokhyl'ko, Wavelet estimators of a density constructed from observations of a mixture, Teor. Imovirnost. Matem. Statist. 70 (2004), 121-130; English transl in Theor. Probability and Math. Statist. 70 (2005), 135-145.
  • 6. A. M. Shcherbina, Estimation of the mean value in a model of mixtures with varying concentrations, Teor. Imovirnost. Matem. Statist. 84 (2011), 142-154; English transl in Theor. Probability and Math. Statist. 84 (2012), 151-164. MR 2857425 (2012h:62130)
  • 7. A. M. Shcherbina, Estimation of the parameters of the binomial distribution in a model of mixture, Teor. Imovirnost. Matem. Statist. 86 (2012), 182-192; English transl in Theor. Probability and Math. Statist. 86 (2013) 205-217. MR 2986460
  • 8. F. Autin and Ch. Pouet, Test on the components of mixture densities, Statistics & Risk Modelling 28 (2011), no. 4, 389-410. MR 2877572
  • 9. L. Bordes, C. Delmas, and P. Vandekerkhove, Semiparametric Estimation of a two-component mixture model where one component is known, Scand. J. Statist. 33 (2006), 733-752. MR 2300913 (2008f:62049)
  • 10. P. Hall and X.-H. Zhou, Nonparametric estimation of component distributions in a multivariable mixture, Ann. Statist. 31 (2003), no. 1, 201-224. MR 1962504 (2003m:62105)
  • 11. R. E. Maiboroda and O. O. Kubaichuk, Improved estimators for moments constructed from observations of a mixture, Theor. Probability and Math. Statist. 70 (2005), 83-92.
  • 12. R. Maiboroda and O. Sugakova, Nonparametric density estimation for symmetric distributions by contaminated data, Metrica 75 (2012), no. 1, 109-126. MR 2878111
  • 13. R. Maiboroda and O. Sugakova, Statistics of mixtures with varying concentrations with application to DNA microarray data analysis, J. Nonparam. Statist. 24 (2012), no. 1, 201-205. MR 2885834
  • 14. R. E. Maiboroda, O. V. Sugakova, and A. V. Doronin, Generalized estimating equations for mixtures with varying concentrations, Canadian J. Statist. 41 (2013), no. 2, 217-236. MR 3061876
  • 15. G. J. McLachlan and D. Peel, Finite Mixture Models, Wiley, New York, 2000. MR 1789474 (2002b:62025)
  • 16. J. Shao, Mathematical statistics, Springer-Verlag, New York, 1998. MR 2002723 (2004g:62002)
  • 17. O. Sugakova, Adaptive estimates for the parameter of a mixture of two symmetric distributions, Theor. Probability and Math. Statist. 82 (2011), 149-159. MR 2790490 (2011m:62130)
  • 18. O. Sugakova, Empirical Bayesian classification for observations with admixture, Theor. Probability and Math. Statist. 84 (2012), 165-172. MR 2857426 (2012f:62128)
  • 19. D. M. Titterington, A. F. Smith, and U. E. Makov, Analysis of Finite Mixture Distributions, Wiley, New York, 1985.

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 62G05, 62G20, 62F12, 62P25, 62G30

Retrieve articles in all journals with MSC (2010): 62G05, 62G20, 62F12, 62P25, 62G30


Additional Information

O. V. Doronin
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
Email: al_doronin@ukr.net

DOI: https://doi.org/10.1090/tpms/950
Keywords: Lower bound, mixture model, generalized estimating equations
Received by editor(s): July 1, 2013
Published electronically: August 6, 2015
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society