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Maximum entropy copula with given diagonal section

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  • Butucea, Cristina
  • Delmas, Jean-François
  • Dutfoy, Anne
  • Fischer, Richard

Abstract

We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal section. We give an explicit criterion on the diagonal section for the existence of the optimal copula and give a closed formula for its entropy. We also provide examples for some diagonal sections of usual bivariate copulas and illustrate the differences between these copulas and the associated maximum entropy copula with the same diagonal section.

Suggested Citation

  • Butucea, Cristina & Delmas, Jean-François & Dutfoy, Anne & Fischer, Richard, 2015. "Maximum entropy copula with given diagonal section," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 61-81.
    • Handle: RePEc:eee:jmvana:v:137:y:2015:i:c:p:61-81
    DOI: 10.1016/j.jmva.2015.01.003
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    References listed on IDEAS

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    1. Nelsen, Roger B. & Molina, José Juan Quesada & Lallena, José Antonio Rodríguez & Flores, Manuel Úbeda, 2004. "Best-possible bounds on sets of bivariate distribution functions," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 348-358, August.
    2. Chu, Ba, 2011. "Recovering copulas from limited information and an application to asset allocation," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1824-1842, July.
    3. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodri­guez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2008. "On the construction of copulas and quasi-copulas with given diagonal sections," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 473-483, April.
    4. Rüschendorf, L. & Thomsen, W., 1993. "Note on the Schrödinger equation and I-projections," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 369-375, August.
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    Cited by:

    1. Arnold, Sebastian & Molchanov, Ilya & Ziegel, Johanna F., 2020. "Bivariate distributions with ordered marginals," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    2. Issey Sukeda & Tomonari Sei, 2025. "On the minimum information checkerboard copula under fixed Kendall’s $$\tau $$ τ," Statistical Papers, Springer, vol. 66(1), pages 1-39, January.

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