IDEAS home Printed from https://ideas.repec.org/a/vrs/demode/v8y2020i1p417-440n16.html
   My bibliography  Save this article

Copula modeling for discrete random vectors

Author

Listed:
  • Geenens Gery

    (School of Mathematics and Statistics, UNSW Sydney, Australia, tel +61 2 938 57032, fax +61 2 9385 7123)

Abstract

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar’s theorem, “the fundamental theorem of copulas”, makes a clear distinction between the continuous case and the discrete case, though. In particular, the copula of a discrete random vector is not fully identifiable, which causes serious inconsistencies. In spite of this, downplaying statements may be found in the related literature, where copula methods are used for modelling dependence between discrete variables. This paper calls to reconsidering the soundness of copula modelling for discrete data. It suggests a more fundamental construction which allows copula ideas to smoothly carry over to the discrete case. Actually it is an attempt at rejuvenating some century-old ideas of Udny Yule, who mentioned a similar construction a long time before copulas got in fashion.

Suggested Citation

  • Geenens Gery, 2020. "Copula modeling for discrete random vectors," Dependence Modeling, De Gruyter, vol. 8(1), pages 417-440, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:417-440:n:16
    DOI: 10.1515/demo-2020-0022
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/demo-2020-0022
    Download Restriction: no
    File URL: https://libkey.io/10.1515/demo-2020-0022?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. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    2. Pfeifer, Dietmar & Nešlehová, Johana, 2004. "Modeling and Generating Dependent Risk Processes for IRM and DFA," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 333-360, November.
    3. Perrone, Elisa & Solus, Liam & Uhler, Caroline, 2019. "Geometry of discrete copulas," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 162-179.
    4. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
    5. Genest, Christian & Nešlehová, Johanna G. & Rémillard, Bruno, 2017. "Asymptotic behavior of the empirical multilinear copula process under broad conditions," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 82-110.
    6. Rüschendorf, L. & Thomsen, W., 1993. "Note on the Schrödinger equation and I-projections," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 369-375, August.
    7. Zilko, Aurelius A. & Kurowicka, Dorota, 2016. "Copula in a multivariate mixed discrete–continuous model," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 28-55.
    8. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650, September.
    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. Rafał Wójcik & Charlie Wusuo Liu, 2022. "Bivariate Copula Trees for Gross Loss Aggregation with Positively Dependent Risks," Risks, MDPI, vol. 10(8), pages 1-24, July.

    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. Geenens Gery, 2020. "Copula modeling for discrete random vectors," Dependence Modeling, De Gruyter, vol. 8(1), pages 417-440, January.
    2. Nagler, Thomas, 2018. "A generic approach to nonparametric function estimation with mixed data," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 326-330.
    3. Jonas Moss & Steffen Grønneberg, 2023. "Partial Identification of Latent Correlations with Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 241-252, March.
    4. César Garcia-Gomez & Ana Pérez & Mercedes Prieto-Alaiz, 2022. "The evolution of poverty in the EU-28: a further look based on multivariate tail dependence," Working Papers 605, ECINEQ, Society for the Study of Economic Inequality.
    5. Aristidis Nikoloulopoulos & Dimitris Karlis, 2010. "Regression in a copula model for bivariate count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1555-1568.
    6. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Siem Jan Koopman & Rutger Lit & André Lucas & Anne Opschoor, 2018. "Dynamic discrete copula models for high‐frequency stock price changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 966-985, November.
    8. Fantazzini, Dean, 2020. "Discussing copulas with Sergey Aivazian: a memoir," MPRA Paper 102317, University Library of Munich, Germany.
    9. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias & Vanduffel Steven, 2016. "Stat Trek. An interview with Christian Genest," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-14, May.
    10. Wei, Zheng & Kim, Daeyoung, 2021. "On exploratory analytic method for multi-way contingency tables with an ordinal response variable and categorical explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    11. Tzougas, George & Makariou, Despoina, 2022. "The multivariate Poisson-Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," LSE Research Online Documents on Economics 117197, London School of Economics and Political Science, LSE Library.
    12. Chavez-Demoulin, V. & Embrechts, P. & Neslehova, J., 2006. "Quantitative models for operational risk: Extremes, dependence and aggregation," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2635-2658, October.
    13. Mai Jan-Frederik & Scherer Matthias, 2013. "What makes dependence modeling challenging? Pitfalls and ways to circumvent them," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 287-306, December.
    14. Pravin Trivedi & David Zimmer, 2017. "A Note on Identification of Bivariate Copulas for Discrete Count Data," Econometrics, MDPI, vol. 5(1), pages 1-11, February.
    15. Kobus, Martyna & Kurek, Radosław, 2018. "Copula-based measurement of interdependence for discrete distributions," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 27-39.
    16. De Backer, Mickael & El Ghouch, Anouar & Van Keilegom, Ingrid, 2016. "Semiparametric Copula Quantile Regression for Complete or Censored Data," LIDAM Discussion Papers ISBA 2016009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Mothafer, Ghasak I.M.A. & Yamamoto, Toshiyuki & Shankar, Venkataraman N., 2018. "A multivariate heterogeneous-dispersion count model for asymmetric interdependent freeway crash types," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 84-105.
    18. Martyna Kobus & Radoslaw Kurek, 2017. "Copula-based measurement of interdependence for discrete distributions," Working Papers 431, ECINEQ, Society for the Study of Economic Inequality.
    19. Marbac, Matthieu & Sedki, Mohammed, 2017. "A family of block-wise one-factor distributions for modeling high-dimensional binary data," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 130-145.
    20. Romera, Rosario & Molanes, Elisa M., 2008. "Copulas in finance and insurance," DES - Working Papers. Statistics and Econometrics. WS ws086321, Universidad Carlos III de Madrid. Departamento de Estadística.

    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:8:y:2020:i:1:p:417-440:n:16. 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.