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Nonparametric Estimation of the Dependence Function in Bivariate Extreme Value Distributions

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  • Jiménez, Javier Rojo
  • Villa-Diharce, Enrique
  • Flores, Miguel
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    Abstract

    The paper considers the problem of estimating the dependence function of a bivariate extreme survival function with standard exponential marginals. Nonparametric estimators for the dependence function are proposed and their strong uniform convergence under suitable conditions is demonstrated. Comparisons of the proposed estimators with other estimators are made in terms of bias and mean squared error. Several real data sets from various applications are used to illustrate the procedures.

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    Bibliographic Info

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

    Volume (Year): 76 (2001)
    Issue (Month): 2 (February)
    Pages: 159-191

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    Handle: RePEc:eee:jmvana:v:76:y:2001:i:2:p:159-191

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    Related research

    Keywords: empirical distribution function; greatest convex minorant; weak convergence; Gaussian process;

    References

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    1. Rojo, J. & Samaniego, F. J., 1994. "Uniform Strong Consistent Estimation of an Ifra Distribution Function," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 150-163, April.
    2. Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
    3. Deheuvels, Paul, 1991. "On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 429-439, November.
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    Cited by:
    1. Gudendorf, Gordon & Segers, Johan, 2011. "Nonparametric estimation of an extreme-value copula in arbitrary dimensions," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 37-47, January.
    2. Falk, Michael & Reiss, Rolf-Dieter, 2005. "On Pickands coordinates in arbitrary dimensions," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 426-453, February.
    3. Falk, Michael & Reiss, Rolf-Dieter, 2005. "On the distribution of Pickands coordinates in bivariate EV and GP models," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 267-295, April.

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