IDEAS home Printed from https://ideas.repec.org/a/vrs/demode/v11y2023i1p19n1.html
   My bibliography  Save this article

Constructing models for spherical and elliptical densities

Author

Listed:
  • Liebscher Eckhard

    (Department of Engineering and Natural Sciences, University of Applied Sciences Merseburg, Eberhard-Leibnitz-Str. 2, 06217 Merseburg, Germany)

Abstract

The article provides construction algorithms for consistent model classes of continuous spherical and elliptical distributions. The algorithms are based on characterization theorems for consistent families of generator functions. This characterization uses the term of complete monotonicity. The algorithms are applied to several examples of generators leading to consistent families of generators with explicit formulas for marginal densities of arbitrary dimension.

Suggested Citation

  • Liebscher Eckhard, 2023. "Constructing models for spherical and elliptical densities," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-19, January.
    • Handle: RePEc:vrs:demode:v:11:y:2023:i:1:p:19:n:1
    DOI: 10.1515/demo-2023-0111
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/demo-2023-0111
    Download Restriction: no
    File URL: https://libkey.io/10.1515/demo-2023-0111?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
    ---><---

    References listed on IDEAS

    as
    1. Yeshunying Wang & Chuancun Yin, 2021. "A New Class of Multivariate Elliptically Contoured Distributions with Inconsistency Property," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1377-1407, December.
    2. Srivastava, M. S. & Bilodeau, M., 1989. "Stein estimation under elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 247-259, February.
    3. Satya Dubey, 1970. "Compound gamma, beta and F distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 16(1), pages 27-31, December.
    4. Liebscher, Eckhard, 2005. "A semiparametric density estimator based on elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 205-225, January.
    5. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    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. 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.
    2. Heather Battey & Oliver Linton, 2013. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," CeMMAP working papers 15/13, Institute for Fiscal Studies.
    3. Heather Battey & Oliver Linton, 2013. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," CeMMAP working papers 41/13, Institute for Fiscal Studies.
    4. Derumigny, A. & Fermanian, J.-D., 2022. "Identifiability and estimation of meta-elliptical copula generators," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    5. Arashi, M. & Kibria, B.M. Golam & Norouzirad, M. & Nadarajah, S., 2014. "Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 53-74.
    6. Falk, Michael, 1998. "A Note on the Comedian for Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 306-317, November.
    7. Kume, Alfred & Hashorva, Enkelejd, 2012. "Calculation of Bayes premium for conditional elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 632-635.
    8. Jacob, P. & Suquet, Ch., 1997. "Regression and asymptotical location of a multivariate sample," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 173-179, September.
    9. Tarpey, Thaddeus, 2000. "Parallel Principal Axes," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 295-313, November.
    10. Isaac E. Cortés & Osvaldo Venegas & Héctor W. Gómez, 2022. "A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    11. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    12. Preinerstorfer, David & Pötscher, Benedikt M., 2017. "On The Power Of Invariant Tests For Hypotheses On A Covariance Matrix," Econometric Theory, Cambridge University Press, vol. 33(1), pages 1-68, February.
    13. Peng Ding, 2016. "On the Conditional Distribution of the Multivariate Distribution," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 293-295, July.
    14. Mittnik, Stefan, 2014. "VaR-implied tail-correlation matrices," Economics Letters, Elsevier, vol. 122(1), pages 69-73.
    15. Jonathan Raimana Chan & Thomas Huckle & Antoine Jacquier & Aitor Muguruza, 2021. "Portfolio optimisation with options," Papers 2111.12658, arXiv.org, revised Sep 2024.
    16. Eckhard Liebscher & Wolf-Dieter Richter, 2016. "Estimation of Star-Shaped Distributions," Risks, MDPI, vol. 4(4), pages 1-37, November.
    17. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    18. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.
    19. Fraiman, Ricardo & Moreno, Leonardo & Ransford, Thomas, 2023. "A Cramér–Wold theorem for elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    20. Arellano-Valle, Reinaldo B., 2001. "On some characterizations of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 227-232, October.

    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:vrs:demode:v:11:y:2023:i:1:p:19:n:1. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.