IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i4p789-810.html
   My bibliography  Save this article

On Riesz and Wishart distributions associated with decomposable undirected graphs

Author

Listed:
  • Andersson, Steen A.
  • Klein, Thomas

Abstract

Classical Wishart distributions on the open convex cone of positive definite matrices and their fundamental features are extended to generalized Riesz and Wishart distributions associated with decomposable undirected graphs using the basic theory of exponential families. The families of these distributions are parameterized by their expectations/natural parameter and multivariate shape parameter and have a non-trivial overlap with the generalized Wishart distributions defined in Andersson and Wojnar (2004) [4] and [8]. This work also extends the Wishart distributions of type I in Letac and Massam (2007) [7] and, more importantly, presents an alternative point of view on the latter paper.

Suggested Citation

  • Andersson, Steen A. & Klein, Thomas, 2010. "On Riesz and Wishart distributions associated with decomposable undirected graphs," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 789-810, April.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:789-810
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00224-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Steen A. Andersson & David Madigan & Michael D. Perlman, 2001. "Alternative Markov Properties for Chain Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 33-85, March.
    2. Andersson, Steen A. & Perlman, Michael D., 1998. "Normal Linear Regression Models With Recursive Graphical Markov Structure," Journal of Multivariate Analysis, Elsevier, vol. 66(2), pages 133-187, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kammoun, Kaouthar & Louati, Mahdi & Masmoudi, Afif, 2017. "Maximum likelihood estimator of the scale parameter for the Riesz distribution," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 127-131.
    2. 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.
    3. Louati, Mahdi & Masmoudi, Afif, 2015. "Moment for the inverse Riesz distributions," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 30-37.
    4. Andre Lucas & Anne Opschoor & Luca Rossini, 2021. "Tail Heterogeneity for Dynamic Covariance Matrices: the F-Riesz Distribution," Tinbergen Institute Discussion Papers 21-010/III, Tinbergen Institute, revised 11 Jul 2023.
    5. 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.
    6. Piotr Graczyk & Hideyuki Ishi & Salha Mamane, 2019. "Wishart exponential families on cones related to tridiagonal matrices," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 439-471, April.

    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. Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
    2. Roberto Colombi & Sabrina Giordano, 2013. "Monotone dependence in graphical models for multivariate Markov chains," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 873-885, October.
    3. Nanny Wermuth & Kayvan Sadeghi, 2012. "Sequences of regressions and their independences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 215-252, June.
    4. S. A. Andersson & G. G. Wojnar, 2004. "Wishart Distributions on Homogeneous Cones," Journal of Theoretical Probability, Springer, vol. 17(4), pages 781-818, October.
    5. Federica Nicolussi & Fulvia Mecatti, 2016. "A smooth subclass of graphical models for chain graph: towards measuring gender gaps," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(1), pages 27-41, January.
    6. Marchetti, Giovanni M., 2006. "Independencies Induced from a Graphical Markov Model After Marginalization and Conditioning: The R Package ggm," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 15(i06).
    7. Castelletti, Federico & Peluso, Stefano, 2021. "Equivalence class selection of categorical graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    8. repec:jss:jstsof:15:i06 is not listed on IDEAS
    9. Vassilios Bazinas & Bent Nielsen, 2022. "Causal Transmission in Reduced-Form Models," Econometrics, MDPI, vol. 10(2), pages 1-25, March.
    10. Johnson, Devin S. & Hoeting, Jennifer A., 2011. "Properties of graphical regression models for multidimensional categorical data," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1471-1475, October.
    11. Drton, Mathias & Andersson, Steen A. & Perlman, Michael D., 2006. "Conditional independence models for seemingly unrelated regressions with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 385-411, February.
    12. Katarzyna Filipiak & Dietrich Rosen, 2012. "On MLEs in an extended multivariate linear growth curve model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1069-1092, November.
    13. Yang Ni & Veerabhadran Baladandayuthapani & Marina Vannucci & Francesco C. Stingo, 2022. "Bayesian graphical models for modern biological applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 197-225, June.
    14. Federico Castelletti, 2020. "Bayesian Model Selection of Gaussian Directed Acyclic Graph Structures," International Statistical Review, International Statistical Institute, vol. 88(3), pages 752-775, 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:eee:jmvana:v:101:y:2010:i:4:p:789-810. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.