Abstract: A sample is observed from a mixture of two symmetric distributions that differ only by the location parameters. We use the method of estimating equations to estimate unknown parameters of the components. The methods works as follows: first, we construct an estimator for the optimal estimating functions; then we use it to construct adaptive estimators. We study the asymptotic behavior of resulting estimators.
R. Maĭboroda and O. Sugakova, Estimation of Euclidean parameters of a mixture of two symmetric distributions, Ukrain. Mat. Zh. 62 (2010), 945-953. (Ukrainian)
R. Maĭboroda, Estimation of mean positions and concentrations from observations of a two-component mixture of symmetric distributions, Teor. Imovir. Mat. Stat. 78 (2008), 132-140; English transl. in Theory Probab. Math. Statist. 78 (2009), 147-156. MR 2446855 (2010b:62134)
O. Sugakova Affiliation:
Department of Mathematics and Theoretical Radiophysics, Faculty for Radiophysics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine