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.
Similar content being viewed by others
References
L. Bordes and S. Mottelet, “Vandekerkhove semiparametric estimation of a two-component mixture model,” Ann. Statist., 34, 1204–1232 (2006).
D. R. Hunter, S. Wang, and T. R. Hettmansperger, “Inference for mixtures of symmetric distributions,” Ann. Statist., 35, 224–251 (2007).
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).
J. Shao, Mathematical Statistics, Springer, New York (1998).
M. Reed and B. Simon, Methods of Modern Mathematical Physics. 1: Functional Analysis [Russian translation], Vol. 1, Mir, Moscow (1977).
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).
I. A. Ibragimov and R. Z. Khas’minskii, Asymptotic Theory of Estimation [in Russian], Nauka, Moscow (1979).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyiMatematychnyi Zhurnal, Vol. 62, No. 7, pp. 945–953, July, 2010.
Rights and permissions
About this article
Cite this article
Maiboroda, R.E., Suhakova, O.V. Estimate for Euclidean parameters of a mixture of two symmetric distributions. Ukr Math J 62, 1098–1108 (2010). https://doi.org/10.1007/s11253-010-0416-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-010-0416-5