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Nonparametric density estimation for symmetric distributions by contaminated data

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Abstract

A semiparametric two-component mixture model is considered, in which the distribution of one (primary) component is unknown and assumed symmetric. The distribution of the other component (admixture) is known. We consider three estimates for the pdf of primary component: a naive one, a symmetrized naive estimate and a symmetrized estimate with adaptive weights. Asymptotic behavior and small sample performance of the estimates are investigated. Some rules of thumb for bandwidth selection are discussed.

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Authors and Affiliations

  1. Department of Probability and Statistics, Faculty of Mechanics and Mathematics, Kyiv National University, Kyiv, Ukraine

    Rostyslav Maiboroda & Olena Sugakova

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

Additional information

Research supported in part by Swedish Institute grant SI-01424/2007.

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Maiboroda, R., Sugakova, O. Nonparametric density estimation for symmetric distributions by contaminated data. Metrika 75, 109–126 (2012). https://doi.org/10.1007/s00184-010-0317-5

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  • DOI: https://doi.org/10.1007/s00184-010-0317-5

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