Kubaychuk O. Statistic Analysis of Characteristics of Random Variables by Observations from Mixture

The characteristics of the random variables by the observations from mixture with the varying concentrations are studied in the thesis. The conditions of the unbiasedness, consistency and asymptotic normality for the linear estimators of the functional moments are found. The consistency, asymptotic normality and efficiency for the adaptive estimators of the functional moments are proved. The algorithms of the correcting of the weighted empirical distribution functions are constructed. The functional limit theorems for the corrected weighted empirical distribution functions are proved. The asymptotic normality of the estimators of the functional moments, which are constructed using the corrected weighted empirical distribution functions, are proved.