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


Ahmadabadi A., Hüdaverdi B.

COMPUTATIONAL STATISTICS, vol.32, no.4, pp.1515-1532, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1007/s00180-017-0750-2
  • Journal Name: COMPUTATIONAL STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1515-1532
  • Keywords: Bivariate extreme value copula, Pickands dependence function, Bernstein copula, Kernel regression, Convexity, EXTREME-VALUE COPULAS, VALUE DISTRIBUTIONS, INFERENCE, BEHAVIOR
  • Dokuz Eylül University Affiliated: Yes

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.