Doronin O. Semiparametric estimation and hypotheses testing on observations from mixture

Different estimators are introduced (the moment, quantile, GEE, and adaptive ones). The asymptotic normality is proved for all mentioned estimators. The consistency is proved for all except the GEE-estimators in general case. The performance of moment, quantile and adaptive estimators is assessed during simulation study. Moreover, the lower bound of dispersion matrix (under unbiasedness condition) is found for GEE- and adaptive estimators. We obtain the theoretically optimal GEE- and adaptive estimators as well. Lower bound of both GEE- and adaptive estimators dispersion matrix is compared with the Fisher informational matrix. Another part of this work is the investigation of the problem of testing hypotheses about mixture distributions functional moments. All proposed approaches work well on simulated data.