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On the Covariance between Functions

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  • Cuadras, C. M.

Abstract

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.

Suggested Citation

  • Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
  • Handle: RePEc:eee:jmvana:v:81:y:2002:i:1:p:19-27
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Wong, Kit Pong, 2013. "Fixed versus variable rate loans under state-dependent preferences," Economic Modelling, Elsevier, vol. 31(C), pages 659-663.
    2. Håkan Selin & Laurent Simula, 2017. "Income Shifting as Income Creation? The Intensive vs. the Extensive Shifting Margins," CESifo Working Paper Series 6510, CESifo Group Munich.
    3. Udo Broll & Kit Wong, 2015. "The impact of inflation risk on forward trading and production," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 14(1), pages 65-73, December.
    4. Cuadras, Carles M. & Cuadras, Daniel, 2008. "Eigenanalysis on a bivariate covariance kernel," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2497-2507, November.
    5. Udo Broll & Kit Wong, 2015. "Trade and cross hedging exchange rate risk," International Economics and Economic Policy, Springer, vol. 12(4), pages 509-520, October.
    6. repec:spr:metrik:v:80:y:2017:i:6:d:10.1007_s00184-017-0620-5 is not listed on IDEAS
    7. Hakan Selin & Laurent Simula, 2017. "Income Creation and/or Income Shifting? The Intensive vs. the Extensive Shifting Margins," Post-Print halshs-01666994, HAL.
    8. Cha, Ji Hwan, 2011. "Comparison of combined stochastic risk processes and its applications," European Journal of Operational Research, Elsevier, vol. 215(2), pages 404-410, December.
    9. 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.
    10. Li, Jingyuan & Liu, Dongri & Wang, Jianli, 2016. "Risk aversion with two risks: A theoretical extension," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 100-105.
    11. Okou, Cedric & Maalaoui Chun, Olfa & Dionne, Georges & Li, Jingyuan, 2016. "Can Higher-Order Risks Explain the Credit Spread Puzzle?," Working Papers 16-1, HEC Montreal, Canada Research Chair in Risk Management.
    12. repec:spr:metrik:v:80:y:2017:i:4:d:10.1007_s00184-017-0613-4 is not listed on IDEAS
    13. Dionne, Georges & Li, Jingyuan, 2014. "Comparative Ross risk aversion in the presence of mean dependent risks," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 128-135.
    14. Kit Wong, 2014. "Production and hedging in futures markets with multiple delivery specifications," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 413-421, October.
    15. Kit Wong, 2014. "Hedging and the competitive firm under correlated price and background risk," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 329-340, October.
    16. 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.
    17. 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.
    18. Dionne, Georges & Li, Jingyuan, 2014. "When can expected utility handle first-order risk aversion?," Journal of Economic Theory, Elsevier, vol. 154(C), pages 403-422.
    19. Georges Dionne & Jingyuan Li & Cedric Okou, 2012. "An Extension of the Consumption-based CAPM Model," Cahiers de recherche 1214, CIRPEE.
    20. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Quadrant Dependent Risks," Cahiers de recherche 1226, CIRPEE.
    21. Ramesh Gupta & Mohammad Tajdari & Henrik Bresinsky, 2008. "Some general results for moments in bivariate distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 173-187, September.
    22. 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.
    23. Broll, Udo & Wong, Kit Pong, 2014. "The impact of inflation risk on forward trading and production," Dresden Discussion Paper Series in Economics 02/14, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    24. 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.

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