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

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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.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Sciences, Dokuz Eylul University, Izmir, Turkey

    Alireza Ahmadabadi & Burcu Hudaverdi Ucer

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  1. Alireza Ahmadabadi
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  2. Burcu Hudaverdi Ucer
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Correspondence to Burcu Hudaverdi Ucer.

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Ahmadabadi, A., Ucer, B.H. Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach. Comput Stat 32, 1515–1532 (2017). https://doi.org/10.1007/s00180-017-0750-2

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  • DOI: https://doi.org/10.1007/s00180-017-0750-2

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