Ukrainian Mathematical Journal

, Volume 62, Issue 7, pp 1098–1108 | Cite as

Estimate for Euclidean parameters of a mixture of two symmetric distributions

  • R. E. Maiboroda
  • O. V. Suhakova

A sample from a mixture of two symmetric distributions is observed. The considered distributions differ only by a shift. Estimates are constructed by the method of estimating equations for parameters of mean locations and concentrations (mixing probabilities) of both components. We obtain conditions for the asymptotic normality of these estimates. The greatest lower bounds for the coefficients of dispersion of the estimates are determined.


Generalize Estimate Equation Asymptotic Normality Generalize Estimate Equation Symmetric Distribution Moment Estimate 
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  1. 1.
    L. Bordes and S. Mottelet, “Vandekerkhove semiparametric estimation of a two-component mixture model,” Ann. Statist., 34, 1204–1232 (2006).zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    D. R. Hunter, S. Wang, and T. R. Hettmansperger, “Inference for mixtures of symmetric distributions,” Ann. Statist., 35, 224–251 (2007).zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    R. Maiboroda, “Estimation of locations and mixing probabilities by observations from two-component mixture of symmetric distributions,” Theor. Probab. Math. Statist., 78, 133–141 (2008).Google Scholar
  4. 4.
    J. Shao, Mathematical Statistics, Springer, New York (1998).Google Scholar
  5. 5.
    M. Reed and B. Simon, Methods of Modern Mathematical Physics. 1: Functional Analysis [Russian translation], Vol. 1, Mir, Moscow (1977).Google Scholar
  6. 6.
    R. Maiboroda and O. Suhakova, “Adaptive estimating equations for the mean position based on observations with addition,” Teor. Imov. Mat. Stat., Issue 80, 91–99 (2009).Google Scholar
  7. 7.
    I. A. Ibragimov and R. Z. Khas’minskii, Asymptotic Theory of Estimation [in Russian], Nauka, Moscow (1979).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • R. E. Maiboroda
    • 1
  • O. V. Suhakova
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyivUkraine

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