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Inference for copula modeling of discrete data: a cautionary tale and some facts

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  • Faugeras Olivier P.

    (Toulouse School of Economics - Université Toulouse Capitole, Manufacture des Tabacs, Bureau MF319, 21 Allée de Brienne, 31000 Toulouse, France)

Abstract

In this note, we elucidate some of the mathematical, statistical and epistemological issues involved in using copulas to model discrete data. We contrast the possible use of (nonparametric) copula methods versus the problematic use of parametric copula models. For the latter, we stress, among other issues, the possibility of obtaining impossible models, arising from model misspecification or unidentifiability of the copula parameter.

Suggested Citation

  • Faugeras Olivier P., 2017. "Inference for copula modeling of discrete data: a cautionary tale and some facts," Dependence Modeling, De Gruyter, vol. 5(1), pages 121-132, January.
    • Handle: RePEc:vrs:demode:v:5:y:2017:i:1:p:121-132:n:8
    DOI: 10.1515/demo-2017-0008
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    References listed on IDEAS

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    1. Faugeras, Olivier P., 2015. "Maximal coupling of empirical copulas for discrete vectors," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 179-186.
    2. Kojadinovic, Ivan, 2017. "Some copula inference procedures adapted to the presence of ties," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 24-41.
    3. Lee, Lung-fei, 2001. "On The Range Of Correlation Coefficients Of Bivariate Ordered Discrete Random Variables," Econometric Theory, Cambridge University Press, vol. 17(1), pages 247-256, February.
    4. 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.
    5. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    6. Faugeras, Olivier P., 2013. "Sklar’s theorem derived using probabilistic continuation and two consistency results," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 271-277.
    7. van Ophem, Hans, 1999. "A General Method To Estimate Correlated Discrete Random Variables," Econometric Theory, Cambridge University Press, vol. 15(2), pages 228-237, April.
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    Cited by:

    1. Faugeras, Olivier & Rüschendorf, Ludger, 2019. "Functional, randomized and smoothed multivariate quantile regions," TSE Working Papers 19-1039, Toulouse School of Economics (TSE), revised Jun 2021.

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