Sampling Bias Correction in the Model of Mixtures with Varying Concentrations

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Abstract

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.

Keywords

Biased sampling Horvitz-Thompson weights Finite mixture model Mixture with varying concentrations Consistency Nonparametric estimation 

AMS 2000 Subject Classification

MSC 62G05 MSC 62D05 MSC 65C60 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematics and Theoretical RadiophysicsTaras Shevchenko National University of KyivKyivUkraine
  2. 2.Department of Probability, Statistics and Actuarial MathematicsTaras Shevchenko National University of KyivKyivUkraine

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