IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v106y2022i4d10.1007_s10182-022-00436-w.html
   My bibliography  Save this article

On the Gaussian representation of the Riesz probability distribution on symmetric matrices

Author

Listed:
  • Abdelhamid Hassairi

    (Laboratory of Probability and Statistics, Department of Mathematics, Faculty of Sciences of Sfax)

  • Fatma Ktari

    (Laboratory of Probability and Statistics, Department of Mathematics, Faculty of Sciences of Sfax)

  • Raoudha Zine

    (Laboratory of Probability and Statistics, Department of Mathematics, Faculty of Sciences of Sfax)

Abstract

The Riesz probability distribution on symmetric matrices represents an important extension of the Wishart distribution. It is defined by its Laplace transform involving the notion of generalized power. Based on the fact that some Wishart distributions are presented by the mean of the multivariate Gaussian distribution, it is shown that some Riesz probability distributions which are not necessarily Wishart are also presented by the mean of Gaussian samples with missing data. As a corollary, we deduce a Gaussian representation of the inverse Riesz distribution and we give its expectation. The results are assessed in simulation studies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:4:d:10.1007_s10182-022-00436-w
    DOI: 10.1007/s10182-022-00436-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-022-00436-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10182-022-00436-w?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. W. B. Smith & R. R. Hocking, 1972. "Wishart Variate Generator," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(3), pages 341-345, November.
    2. Tounsi, Mariem & Zine, Raoudha, 2012. "The inverse Riesz probability distribution on symmetric matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 174-182.
    3. 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.
    4. A. Hassairi & S. Lajmi, 2001. "Riesz Exponential Families on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 14(4), pages 927-948, October.
    5. Louati, Mahdi & Masmoudi, Afif, 2015. "Moment for the inverse Riesz distributions," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 30-37.
    6. 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.
    7. Hao, Jian & Krishnamoorthy, K., 2001. "Inferences on a Normal Covariance Matrix and Generalized Variance with Monotone Missing Data," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 62-82, July.
    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. 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.
    2. 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.
    3. 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.
    4. Anne Opschoor & Dewi Peerlings & Luca Rossini & Andre Lucas, 2024. "Density Forecasting for Electricity Prices under Tail Heterogeneity with the t-Riesz Distribution," Tinbergen Institute Discussion Papers 24-049/III, Tinbergen Institute.
    5. Louati, Mahdi & Masmoudi, Afif, 2015. "Moment for the inverse Riesz distributions," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 30-37.
    6. Emna Ghorbel & Mahdi Louati, 2024. "An expectation maximization algorithm for the hidden markov models with multiparameter student-t observations," Computational Statistics, Springer, vol. 39(6), pages 3287-3301, September.
    7. Clement Stone & Michael Sobel, 1990. "The robustness of estimates of total indirect effects in covariance structure models estimated by maximum," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 337-352, June.
    8. Yutaka Kano, 1990. "Noniterative estimation and the choice of the number of factors in exploratory factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 277-291, June.
    9. Tsukada, Shin-ichi, 2024. "Hypothesis testing for mean vector and covariance matrix of multi-populations under a two-step monotone incomplete sample in large sample and dimension," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    10. Tsukada, Shin-ichi, 2014. "Equivalence testing of mean vector and covariance matrix for multi-populations under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 183-196.
    11. Abdelkoddousse Ahdida & Aurélien Alfonsi, 2013. "Exact and high order discretization schemes for Wishart processes and their affine extensions," Post-Print hal-00491371, HAL.
    12. Bernhard Flury & Martin Schmid & A. Narayanan, 1994. "Error rates in quadratic discrimination with constraints on the covariance matrices," Journal of Classification, Springer;The Classification Society, vol. 11(1), pages 101-120, March.
    13. 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.
    14. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    15. Kurita, Eri & Seo, Takashi, 2022. "Multivariate normality test based on kurtosis with two-step monotone missing data," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    16. Lu, Nelson & Zimmerman, Dale L., 2005. "The likelihood ratio test for a separable covariance matrix," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 449-457, July.
    17. Nobile, Agostino, 2000. "Comment: Bayesian multinomial probit models with a normalization constraint," Journal of Econometrics, Elsevier, vol. 99(2), pages 335-345, December.
    18. Mariem Tounsi, 2020. "The Extended Matrix-Variate Beta Probability Distribution on Symmetric Matrices," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 647-676, June.
    19. Nobumichi Shutoh & Takahiro Nishiyama & Masashi Hyodo, 2017. "Bartlett correction to the likelihood ratio test for MCAR with two-step monotone sample," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(3), pages 184-199, August.
    20. Tsukada, Shin-ichi, 2014. "Asymptotic expansion for distribution of the trace of a covariance matrix under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 206-219.

    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:alstar:v:106:y:2022:i:4:d:10.1007_s10182-022-00436-w. 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.