Sampling Bias Correction in the Model of Mixtures with Varying Concentrations

Model of mixture with varying concentrations is a generalization of the classical finite mixture model in which the mixing probabilities (concentrations) vary from observation to observation. We consider the case when the concentrations of the mixture components are known, but no assumptions on the distributions of the observed variable are made. The problem is to estimate the moments of the components’ distributions. We propose a modification of the Horvitz-Thompson weighting for moments estimation by observations from mixture with varying concentrations in presence of sampling bias. Consistency of obtained estimators is demonstrated. Results of simulations are presented.