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Some new results on the empirical copula estimator with applications

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  • Swanepoel, J.W.H.
  • Allison, J.S.

Abstract

We derive the joint distribution of the ranks associated with a given bivariate random sample. Using these results, exact non-asymptotic expressions and asymptotic expansions for the mean and variance of the classical empirical copula estimator are obtained. An explicit expression of the coefficient appearing in the O(1/n)-term for the mean can, for example, be found; a result that apparently does not appear in the existing literature. Furthermore, it is shown that similar explicit non-asymptotic expressions as well as asymptotic expansions can be derived for the rank-based Bernstein copula estimator.

Suggested Citation

  • Swanepoel, J.W.H. & Allison, J.S., 2013. "Some new results on the empirical copula estimator with applications," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1731-1739.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:7:p:1731-1739
    DOI: 10.1016/j.spl.2013.03.027
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    References listed on IDEAS

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    1. Huang, Jen-Jsung & Lee, Kuo-Jung & Liang, Hueimei & Lin, Wei-Fu, 2009. "Estimating value at risk of portfolio by conditional copula-GARCH method," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 315-324, December.
    2. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
    3. Gerda Claeskens & Rosemary Nguti & Paul Janssen, 2008. "One-sided tests in shared frailty models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 69-82, May.
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    Cited by:

    1. Shih, Jia-Han & Emura, Takeshi, 2021. "On the copula correlation ratio and its generalization," Journal of Multivariate Analysis, Elsevier, vol. 182(C).

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