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Contributions to the diagonal expansion of a bivariate copula with continuous extensions

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  • Cuadras, Carles M.

Abstract

We find some properties and eigendecompositions of two integral operators related to copulas. By using an inner product between two functions via an extension of the covariance, we study the countable set of eigenpairs, which is related to the set of canonical correlations and functions. Then a canonical analysis on the so-called Cuadras–Augé family of copulas is performed, showing the continuous dimensionality of this distribution. A diagonal expansion in terms of an integral is obtained. As a consequence, this continuous expansion allows us to generate a wide family of copulas.

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  • Cuadras, Carles M., 2015. "Contributions to the diagonal expansion of a bivariate copula with continuous extensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 28-44.
    • Handle: RePEc:eee:jmvana:v:139:y:2015:i:c:p:28-44
    DOI: 10.1016/j.jmva.2015.02.015
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    References listed on IDEAS

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    1. Cuadras, Carles M., 2010. "Letter to the Editor," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1317-1318, May.
    2. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
    3. Cuadras, Carles M. & Cuadras, Daniel, 2008. "Eigenanalysis on a bivariate covariance kernel," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2497-2507, November.
    4. Ruiz-Rivas, Carmen & Cuadras, Carles M., 1988. "Inference properties of a one-parameter curved exponential family of distributions with given marginals," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 447-456, November.
    5. Cuadras, C. M. & Fortiana, J., 1995. "A Continuous Metric Scaling Solution for a Random Variable," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 1-14, January.
    6. Durante, Fabrizio & Okhrin, Ostap, 2014. "Estimation procedures for exchangeable Marshall copulas with hydrological application," SFB 649 Discussion Papers 2014-014, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Gardner, Sugnet & Gower, John C. & le Roux, N.J., 2006. "A synthesis of canonical variate analysis, generalised canonical correlation and Procrustes analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 107-134, January.
    8. Ali, Mir M. & Mikhail, N. N. & Haq, M. Safiul, 1978. "A class of bivariate distributions including the bivariate logistic," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 405-412, September.
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    Cited by:

    1. Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2021. "New results on perturbation-based copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 347-373, January.
    2. Cuadras, Carles M. & Greenacre, Michael, 2022. "A short history of statistical association: From correlation to correspondence analysis to copulas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Grothe Oliver & Rieger Jonas, 2024. "Decomposition and graphical correspondence analysis of checkerboard copulas," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-31.
    4. Walter Diaz & Carles M. Cuadras, 2022. "An extension of the Gumbel–Barnett family of copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 913-926, October.
    5. Lo, Ambrose, 2017. "Functional generalizations of Hoeffding’s covariance lemma and a formula for Kendall’s tau," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 218-226.
    6. Hakim Bekrizadeh & Babak Jamshidi, 2017. "A new class of bivariate copulas: dependence measures and properties," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 31-50, April.

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