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Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach

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  • Alireza Ahmadabadi

    (Dokuz Eylul University)

  • Burcu Hudaverdi Ucer

    (Dokuz Eylul University)

Abstract

In this study, a new nonparametric approach using Bernstein copula approximation is proposed to estimate Pickands dependence function. New data points obtained with Bernstein copula approximation serve to estimate the unknown Pickands dependence function. Kernel regression method is then used to derive an intrinsic estimator satisfying the convexity. Some extreme-value copula models are used to measure the performance of the estimator by a comprehensive simulation study. Also, a real-data example is illustrated. The proposed Pickands estimator provides a flexible way to have a better fit and has a better performance than the conventional estimators.

Suggested Citation

  • Alireza Ahmadabadi & Burcu Hudaverdi Ucer, 2017. "Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach," Computational Statistics, Springer, vol. 32(4), pages 1515-1532, December.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-017-0750-2
    DOI: 10.1007/s00180-017-0750-2
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    References listed on IDEAS

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    1. Néstor Aguilera & Liliana Forzani & Pedro Morin, 2011. "On uniform consistent estimators for convex regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 897-908.
    2. Sancetta, Alessio, 2007. "Nonparametric estimation of distributions with given marginals via Bernstein-Kantorovich polynomials: L1 and pointwise convergence theory," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1376-1390, August.
    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.
    4. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    5. 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.
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