Estimation of the mean value in a model of mixtures with varying concentrations
Andrey Shcherbina · Theory of Probability and Mathematical Statistics · 2012
We consider a model for observations sampled from a two-component mixture. A certain numerical characteristic corresponds to every object. The distribution of the characteristic is unknown. The observations are obtained by sampling objects belonging to several groups. This procedure results in dependences among characteristics of objects, which constitute the difference between this setting and the classical one. The total amount of objects of the first and second class in each group is known, while the classes of objects are unknown. We consider the problem of estimation of mean values for characteristics of objects in each class. Two different settings are considered and expressions for the mean square errors are obtained for each of the settings. We show that the corresponding estimators are consistent and asymptotically normal.