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Classification of Riesz Exponential Families on a Symmetric Cone by Invariance Properties

Author

Listed:
  • A. Hassairi

    (Faculté des Sciences de Sfax)

  • S. Lajmi

    (Faculté des Sciences de Sfax)

Abstract

Letac(5) has characterized the Wishart natural exponential families (NEFs) on the symmetric cone Ω of a Jordan algebra E by invariance under a group G of automorphisms of E preserving Ω. Hassairi and Lajmi(4) have introduced the so called Riesz NEF's as an extension of the Wishart NEF's and they have characterized them by invariance under the triangular group T. Pursuing these classifications, we construct a class of subgroups of G containing the triangular group T and we use them to classify the Riesz NEFs on Ω and therefore to characterize each class by an invariance property.

Suggested Citation

  • A. Hassairi & S. Lajmi, 2004. "Classification of Riesz Exponential Families on a Symmetric Cone by Invariance Properties," Journal of Theoretical Probability, Springer, vol. 17(3), pages 521-539, July.
    • Handle: RePEc:spr:jotpro:v:17:y:2004:i:3:d:10.1023_b:jotp.0000040287.87081.ba
    DOI: 10.1023/B:JOTP.0000040287.87081.ba
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    References listed on IDEAS

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    1. Hélène Massam & Erhard Neher, 1997. "On Transformations and Determinants of Wishart Variables on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 10(4), pages 867-902, October.
    2. A. Hassairi & S. Lajmi, 2001. "Riesz Exponential Families on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 14(4), pages 927-948, October.
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