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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.

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Authors and Affiliations

  1. Department of Mathematics and Theoretical Radiophysics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Olena Sugakova

  2. Department of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Rostyslav Maiboroda

Authors
  1. Olena Sugakova
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  2. Rostyslav Maiboroda
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Correspondence to Rostyslav Maiboroda.

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Sugakova, O., Maiboroda, R. Sampling Bias Correction in the Model of Mixtures with Varying Concentrations. Methodol Comput Appl Probab 17, 223–234 (2015). https://doi.org/10.1007/s11009-013-9349-4

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  • DOI: https://doi.org/10.1007/s11009-013-9349-4

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