Journals / Türkiye İstatistik Derneği İstatistik Dergisi / 2022 / Volume: 14 Issue: 2

A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function

Selim Orhun Susam(MUNZUR UNIVERSITY)
Pages
—
Publication Date
2022-12-31
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, the graphical method is illustrated by a real data example.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We present a graphical tool that was primarily proposed by Michiels et al. [18] and later modified by Durante et al. [4].
📊
Key Findings & Data:We conduct a Monte Carlo simulation study to investigate its performance.
💡
Conclusion & Impact:Also, the graphical method is illustrated by a real data example.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Copula · Pickands function · Extreme value copula

Abstract

We present a graphical tool that was primarily proposed by Michiels et al. [18] and later modified by Durante et al. [4]. We also improve this method to select the better fit of the given data among some extreme value copulas based on the Pickands dependence function. We conduct a Monte Carlo simulation study to investigate its performance. Also, the graphical method is illustrated by a real data example.

🔖

Cite This Article

Susam, S. O. (2022). A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function. Türkiye İstatistik Derneği İstatistik Dergisi, Volume: 14 Issue: 2. https://ajindex.com/articles/1562007

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (21)

  1. Ahmadabadi, A. and Ucer, B.H. (2017). Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach. Computitional Statistics, 32, 1515-1532.
  2. Brechmann, E.C. (2013). Properties of extreme-value copulas. [Thesis, Technical University of Munich].
  3. Capéraà, P., Fougres, A.L. and Genest, C. (1997). A nonparametric estimation procedure for bivariate extreme value copulas. Biometrika, 84, 567-577.
  4. Durante, F., Fernández-Sánchez, J. and Pappad´a, R. (2015). Copulas, diagonals and tail dependence. Fuzzy Sets and Systems, 264, 22-41.
  5. Dutfoy, A., Parey, S. and Roche, N. (2017). Multivariate extreme value theory-A tutorial with applications to hydrology and meteorology. Dependence Modeling, 2, 30-48.
  6. Frees, E. and Valdez, E. (1998). Understanding relationships using copulas. North American Actuarial Journal, 2, 1-25.
  7. Galambos, J. (1975). Order statistics of samples from multivariate distributions. Journal of the American Statistical Association, 70, 674-680.
  8. Genest, C., Kojadinovic, I., Néslehová, J. and Yan, J. (2011). A goodness-of-fit test for bivariate extremevalue copulas. Bernoulli, 17(1), 253-275.
  9. Genest, C. and Segers, J. (2009). Rank-Based inference for bivariate extreme value copulas. The Annals of Statistics, 37, 2990-3022.
  10. Gudendorf, G. and Segers, J. (2011). Nonparametric estimation of an extreme-value copula in arbitrary dimensions. Journal of Multivariate Analysis, 102(1), 37-47.
  11. Guillotte, S. and Perron, F. (2016). Polynomial pickands functions. Bernoulli, 22(1), 213-241.
  12. Gumbel, E.J. (1960). Distributios des valeurs extr´emes en plusiers dimensions. Publications de l’Institut de Statistique de l’Université de Paris, 9, 171-173.
  13. Hougaard, P. (1986). A class of multivariate failure time distributions. Biometrika, 73, 671-678.
  14. Husler, J. (1986). Extreme values of non-stationary random sequences. Journal of Applied Probability, 23, 937-950.
  15. Joe, H. (1990). Multivariate concordance. Journal of Multivariate Analysis, 35, 12-30.
  16. Marcon, G., Padoan, S.A. and Antoniano-Villalobos, I. (2016). Bayesian inference for the extremal dependence. Electronic Journal of Statistics, 10(2), 3310-3337.
  17. Marcon, G., Padoan, S.A., Naveau, P., Muliere, P. and Segers, J. (2017). Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials. Journal of Statistical Planning and Inference, 183, 1-17.
  18. Michiels, F. and De Schepper, A. (2013). A new graphical tool for copula selection. Journal of Computational and Graphical Statistics, 22(2), 471-493.
  19. Pickands, J. (1981). Multivariate extreme value distribution. In Proceedings of the International Statistical Institute, 859-878.
  20. Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges. Publications de lInstitut de Statistique de lUniversite de Paris, 8, 229-231.
  21. Vettori, S., Huser, R. and Genton, M.G. (2018). A comparison of dependence function estimators in multivariate extremes. Statistics and Computing, 28(3), 525-538.