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Identifiability of Finite Mixtures of Elliptical Distributions

Author

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  • HAJO HOLZMANN
  • AXEL MUNK
  • TILMANN GNEITING

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..

Suggested Citation

  • Hajo Holzmann & Axel Munk & Tilmann Gneiting, 2006. "Identifiability of Finite Mixtures of Elliptical Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 753-763.
  • Handle: RePEc:bla:scjsta:v:33:y:2006:i:4:p:753-763
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    Cited by:

    1. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
    2. Galimberti, Giuliano & Soffritti, Gabriele, 2014. "A multivariate linear regression analysis using finite mixtures of t distributions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 138-150.
    3. Battey, Heather & Linton, Oliver, 2014. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 43-67.
    4. repec:eee:csdana:v:113:y:2017:i:c:p:475-496 is not listed on IDEAS
    5. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    6. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi-dimensional log-concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607.
    7. Holzmann, Hajo & Schwaiger, Florian, 2016. "Testing for the number of states in hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 318-330.
    8. Erik Meijer & Jelmer Ypma, 2008. "A Simple Identification Proof for a Mixture of Two Univariate Normal Distributions," Journal of Classification, Springer;The Classification Society, vol. 25(1), pages 113-123, June.
    9. repec:eee:jmvana:v:161:y:2017:i:c:p:141-156 is not listed on IDEAS

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