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Identifiability of Finite Mixtures of Elliptical Distributions

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  • HAJO HOLZMANN
  • AXEL MUNK
  • TILMANN GNEITING
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    Abstract

    We present general results on the identifiability of finite mixtures of elliptical distributions under conditions on the characteristic generators or density generators. Examples include the multivariate "t"-distribution, symmetric stable laws, exponential power and Kotz distributions. In each case, the shape parameter is allowed to vary in the mixture, in addition to the location vector and the scatter matrix. Furthermore, we discuss the identifiability of finite mixtures of elliptical densities with generators that correspond to scale mixtures of normal distributions. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..

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    Bibliographic Info

    Article provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

    Volume (Year): 33 (2006)
    Issue (Month): 4 ()
    Pages: 753-763

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    Handle: RePEc:bla:scjsta:v:33:y:2006:i:4:p:753-763

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    Cited by:
    1. Erik Meijer & Jelmer Ypma, 2008. "A Simple Identification Proof for a Mixture of Two Univariate Normal Distributions," Journal of Classification, Springer, Springer, vol. 25(1), pages 113-123, June.
    2. Galimberti, Giuliano & Soffritti, Gabriele, 2014. "A multivariate linear regression analysis using finite mixtures of t distributions," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 71(C), pages 138-150.
    3. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(1), pages 126-142, January.
    4. Battey, Heather & Linton, Oliver, 2014. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 123(C), pages 43-67.

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