IDEAS home Printed from https://ideas.repec.org/a/vrs/demode/v11y2023i1p12n1.html
   My bibliography  Save this article

Characterization of pre-idempotent Copulas

Author

Listed:
  • Chamnan Wongtawan

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

  • Sumetkijakan Songkiat

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

Abstract

Copulas C C for which ( C t C ) 2 = C t C {({C}^{t}C)}^{2}={C}^{t}C are called pre-idempotent copulas, of which well-studied examples are idempotent copulas and complete dependence copulas. As such, we shall work mainly with the topology induced by the modified Sobolev norm, with respect to which the class ℛ {\mathcal{ {\mathcal R} }} of pre-idempotent copulas is closed and the class of factorizable copulas is a dense subset of ℛ {\mathcal{ {\mathcal R} }} . Identifying copulas with Markov operators on L 2 {L}^{2} , the one-to-one correspondence between pre-idempotent copulas and partial isometries is one of our main tools. In the same spirit as Darsow and Olsen’s work on idempotent copulas, we obtain an explicit characterization of pre-idempotent copulas, which is split into cases according to the atomicity of its associated σ \sigma -algebras, where the nonatomic case gives all factorizable copulas and the totally atomic case yields conjugates of ordinal sums of copies of the product copula.

Suggested Citation

  • Chamnan Wongtawan & Sumetkijakan Songkiat, 2023. "Characterization of pre-idempotent Copulas," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-12, January.
  • Handle: RePEc:vrs:demode:v:11:y:2023:i:1:p:12:n:1
    DOI: 10.1515/demo-2023-0106
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/demo-2023-0106
    Download Restriction: no

    File URL: https://libkey.io/10.1515/demo-2023-0106?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. Karl Siburg & Pavel Stoimenov, 2010. "A measure of mutual complete dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 239-251, March.
    2. Printechapat, Tanes & Sumetkijakan, Songkiat, 2018. "Factorizable non-atomic copulas," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 86-94.
    3. Piotr Mikusiński & Michael Taylor, 2010. "Some approximations of n-copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 385-414, November.
    4. Nattakarn Chaidee & Tippawan Santiwipanont & Songkiat Sumetkijakan, 2016. "Patched approximations and their convergence," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(9), pages 2654-2664, May.
    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. Durante, Fabrizio & Sánchez, Juan Fernández, 2012. "On the approximation of copulas via shuffles of Min," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1761-1767.
    2. Shih, Jia-Han & Emura, Takeshi, 2021. "On the copula correlation ratio and its generalization," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    3. Griessenberger Florian & Trutschnig Wolfgang, 2022. "Maximal asymmetry of bivariate copulas and consequences to measures of dependence," Dependence Modeling, De Gruyter, vol. 10(1), pages 245-269, January.
    4. Durante Fabrizio & Fernández-Sánchez Juan & Trutschnig Wolfgang, 2014. "Solution to an open problem about a transformation on the space of copulas," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-8, November.
    5. Ansari Jonathan & Rüschendorf Ludger, 2021. "Sklar’s theorem, copula products, and ordering results in factor models," Dependence Modeling, De Gruyter, vol. 9(1), pages 267-306, January.
    6. Lai, Tingyu & Zhang, Zhongzhan & Wang, Yafei & Kong, Linglong, 2021. "Testing independence of functional variables by angle covariance," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    7. Durante, Fabrizio & Fernández Sánchez, Juan & Trutschnig, Wolfgang, 2014. "Multivariate copulas with hairpin support," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 323-334.
    8. Ansari Jonathan & Rüschendorf Ludger, 2018. "Ordering risk bounds in factor models," Dependence Modeling, De Gruyter, vol. 6(1), pages 259-287, November.
    9. Fabrizio Durante & Juan Fernández Sánchez & Wolfgang Trutschnig, 2020. "Spatially homogeneous copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 607-626, April.
    10. Coblenz, Maximilian & Grothe, Oliver & Schreyer, Manuela & Trutschnig, Wolfgang, 2018. "On the length of copula level curves," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 347-365.
    11. Harder, Michael & Stadtmüller, Ulrich, 2014. "Maximal non-exchangeability in dimension d," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 31-41.
    12. Karl Siburg & Pavel Stoimenov, 2015. "Almost opposite regression dependence in bivariate distributions," Statistical Papers, Springer, vol. 56(4), pages 1033-1039, November.

    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:12: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.