Estimation of mean positions and concentrations from observations of a two-component mixture of symmetric distributions
Rostyslav Maiboroda · Theory of Probability and Mathematical Statistics · 2009
A statistician observes a sample from a mixture of two symmetric distributions that differ from one another by a shift parameter. Estimators for mean position parameters and concentrations (mixing probabilities) for both components are constructed by the method of moments. Conditions for the consistence and asymptotic normality of these estimators are obtained. The asymptotic variance (dispersion coefficient) of the estimator of the concentration is found.