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On the Covariance between Functions


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  • Cuadras, C. M.
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    The covariance between the functions of two random variables is obtained in terms of the cumulative distribution function. This result generalizes previous formulae given by W. Hoeffding (1940, Schriften Math. Inst. Univ. Berlin5, 181-233) and K. V. Mardia (1967, Biometrika54, 235-249). An expansion for the covariance, an inequality, a maximum correlation and other consequences are obtained from this generalization.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 81 (2002)
    Issue (Month): 1 (April)
    Pages: 19-27

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    Handle: RePEc:eee:jmvana:v:81:y:2002:i:1:p:19-27

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    Keywords: Hoeffding's lemma given marginals generalized covariance covariance expansion Heaviside distribution maximum correlation;


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    1. 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.
    2. Cuadras, C. M., 1992. "Probability distributions with given multivariate marginals and given dependence structure," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 51-66, July.
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    Cited by:
    1. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Mean Dependent Risks," Cahiers de recherche 1211, CIRPEE.
    2. Dewan, Isha & Rao, B.L.S. Prakasa, 2005. "Wilcoxon-signed rank test for associated sequences," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 131-142, February.
    3. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Quadrant Dependent Risks," Cahiers de recherche 1226, CIRPEE.
    4. Wong, Kit Pong, 2013. "Fixed versus variable rate loans under state-dependent preferences," Economic Modelling, Elsevier, vol. 31(C), pages 659-663.
    5. Cuadras, Carles M. & Cuadras, Daniel, 2008. "Eigenanalysis on a bivariate covariance kernel," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2497-2507, November.
    6. Georges Dionne & Jingyuan Li & Cedric Okou, 2012. "An Extension of the Consumption-based CAPM Model," Cahiers de recherche 1214, CIRPEE.
    7. Beare, Brendan K., 2009. "A generalization of Hoeffding's lemma, and a new class of covariance inequalities," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 637-642, March.
    8. Ramesh Gupta & Mohammad Tajdari & Henrik Bresinsky, 2008. "Some general results for moments in bivariate distributions," Metrika, Springer, vol. 68(2), pages 173-187, September.
    9. Li, Jingyuan, 2011. "The demand for a risky asset in the presence of a background risk," Journal of Economic Theory, Elsevier, vol. 146(1), pages 372-391, January.


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