, Volume 75, Issue 1, pp 109–126

Nonparametric density estimation for symmetric distributions by contaminated data



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.


Asymptotic normality Finite mixture model Symmetric distribution Kernel density estimate Rule of thumb MISE 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Probability and Statistics, Faculty of Mechanics and MathematicsKyiv National UniversityKyivUkraine

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