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Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known

Author

Listed:
  • Segers, J.J.J.

    (Tilburg University, Center For Economic Research)

  • van den Akker, R.

    (Tilburg University, Center For Economic Research)

  • Werker, B.J.M.

    (Tilburg University, Center For Economic Research)

Abstract

At the heart of the copula methodology in statistics is the idea of separating marginal distributions from the dependence structure. However, as shown in this paper, this separation is not to be taken for granted: in the model where the copula is known and the marginal distributions are completely unknown, the empirical distribution functions are semiparametrically efficient if and only if the copula is the independence copula. Incorporating the knowledge of the copula into a nonparametric likelihood yields an estimation procedure which by simulations is shown to outperform the empirical distribution functions, the amount of improvement depending on the copula. Although the known-copula model is arguably artificial, it provides an instructive stepping stone to the more general model of a parametrically specified copula and arbitrary margins.

Suggested Citation

  • Segers, J.J.J. & van den Akker, R. & Werker, B.J.M., 2008. "Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known," Discussion Paper 2008-40, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:950a8cda-8f8c-43a9-a5c2-88ca22b891da
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/982459/2008-40.pdf
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    References listed on IDEAS

    as
    1. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
    2. van den Akker, R., 2007. "Integer-valued time series," Other publications TiSEM e7f68743-db57-4056-9ca7-1, Tilburg University, School of Economics and Management.
    3. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    4. Drost, Feike C. & van den Akker, Ramon & Werker, Bas J.M., 2008. "Note on integer-valued bilinear time series models," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 992-996, June.
    5. Peng, Hanxiang & Schick, Anton, 2002. "On efficient estimation of linear functionals of a bivariate distribution with known marginals," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 83-91, August.
    6. Peng, Hanxiang & Schick, Anton, 2005. "Efficient estimation of linear functionals of a bivariate distribution with equal, but unknown marginals: the least-squares approach," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 385-409, August.
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    More about this item

    Keywords

    independence copula; nonparametric maximum likelihood estimator; score function; semiparametric efficiency; tangent space;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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