IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v17y2004i3d10.1023_bjotp.0000040287.87081.ba.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/B:JOTP.0000040287.87081.ba
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/B:JOTP.0000040287.87081.ba?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christa Cuchiero & Martin Keller-Ressel & Eberhard Mayerhofer & Josef Teichmann, 2016. "Affine Processes on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 29(2), pages 359-422, June.
    2. S. A. Andersson & G. G. Wojnar, 2004. "Wishart Distributions on Homogeneous Cones," Journal of Theoretical Probability, Springer, vol. 17(4), pages 781-818, October.
    3. A. Hassairi & S. Lajmi & R. Zine, 2008. "A Characterization of the Riesz Probability Distribution," Journal of Theoretical Probability, Springer, vol. 21(4), pages 773-790, December.
    4. Zmyślony Roman & Kozioł Arkadiusz, 2019. "Testing Hypotheses About Structure Of Parameters In Models With Block Compound Symmetric Covariance Structure," Statistics in Transition New Series, Polish Statistical Association, vol. 20(2), pages 139-153, June.
    5. Bartosz Kołodziejek, 2016. "The Lukacs–Olkin–Rubin Theorem on Symmetric Cones Without Invariance of the “Quotient”," Journal of Theoretical Probability, Springer, vol. 29(2), pages 550-568, June.
    6. Gribisch, Bastian & Hartkopf, Jan Patrick, 2023. "Modeling realized covariance measures with heterogeneous liquidity: A generalized matrix-variate Wishart state-space model," Journal of Econometrics, Elsevier, vol. 235(1), pages 43-64.
    7. Abdelhamid Hassairi & Fatma Ktari & Raoudha Zine, 2022. "On the Gaussian representation of the Riesz probability distribution on symmetric matrices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 609-632, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jotpro:v:17:y:2004:i:3:d:10.1023_b:jotp.0000040287.87081.ba. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.