An asymptotically effective estimate of a distribution from a sample with varying mixture (Q2740454)

Problems of analysis of mixtures with changing concentrations often arise under processing of economical, medico-biological and sociological data. The aim of this paper is to construct asymptotically efficient estimators for discrete distributions of components of mixtures in the case of well-known concentrations. As example, a problem of sociological analysis of results of an election is considered. Consider the observations \(\xi_{1},\dots,\xi_{N},\) which are independent discrete r.v.s with distribution NEWLINE\[NEWLINEP(\xi_{i}=l)=\sum_{m=1}^{M}w_{i}^{m}H_{l,m},NEWLINE\]NEWLINE where \(w_{i}^{m}\) are given, and \(H_{l,m}\) are to be estimated. Asymptotically efficient estimators for \(H_{l,m}\) are constructed.