Estimation of Concentrations Parameters in the Model of Mixture with Varying Concentrations

Abstract

Model of Mixture with Varying Concentrations (MVC) is a generalization of the finite mixture model (FMM) at which the mixing probabilities (concentrations of components in the mixture) vary from observation to observation. In this paper we assume that the components' distributions are completely unknown, while the concentrations are known up to some unknown euclidean parameter. Two approaches are considered to the semiparametric estimation of this parameter in the case of two-component mixture. The Least Squares (LS) estimator is based on fitting the distribution functions of the observations. The Empirical Maximum Likelihood estimator (EML) utilizes some empirical version of the likelihood function.
Consistency of the LS estimator is demonstrated. A fast algorithm for the LS estimator calculation is presented. EML and LS estimators are compared via simulations. Both EML and LS estimators show sufficiently good performance in all the experiments. The LS estimator performed better then the EML one for components with different variance. The EML estimator outperformed the LS one for nongaussian components with asymmetric tails.