Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 14 Sayı: 2, 38 - 50, 31.12.2022

Öz

Kaynakça

  • 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.
  • Brechmann, E.C. (2013). Properties of extreme-value copulas. [Thesis, Technical University of Munich].
  • Capéraà, P., Fougres, A.L. and Genest, C. (1997). A nonparametric estimation procedure for bivariate extreme value copulas. Biometrika, 84, 567-577.
  • Durante, F., Fernández-Sánchez, J. and Pappad´a, R. (2015). Copulas, diagonals and tail dependence. Fuzzy Sets and Systems, 264, 22-41.
  • 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.
  • Frees, E. and Valdez, E. (1998). Understanding relationships using copulas. North American Actuarial Journal, 2, 1-25.
  • Galambos, J. (1975). Order statistics of samples from multivariate distributions. Journal of the American Statistical Association, 70, 674-680.
  • Genest, C., Kojadinovic, I., Néslehová, J. and Yan, J. (2011). A goodness-of-fit test for bivariate extremevalue copulas. Bernoulli, 17(1), 253-275.
  • Genest, C. and Segers, J. (2009). Rank-Based inference for bivariate extreme value copulas. The Annals of Statistics, 37, 2990-3022.
  • Gudendorf, G. and Segers, J. (2011). Nonparametric estimation of an extreme-value copula in arbitrary dimensions. Journal of Multivariate Analysis, 102(1), 37-47.
  • Guillotte, S. and Perron, F. (2016). Polynomial pickands functions. Bernoulli, 22(1), 213-241.
  • 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.
  • Hougaard, P. (1986). A class of multivariate failure time distributions. Biometrika, 73, 671-678.
  • Husler, J. (1986). Extreme values of non-stationary random sequences. Journal of Applied Probability, 23, 937-950.
  • Joe, H. (1990). Multivariate concordance. Journal of Multivariate Analysis, 35, 12-30.
  • Marcon, G., Padoan, S.A. and Antoniano-Villalobos, I. (2016). Bayesian inference for the extremal dependence. Electronic Journal of Statistics, 10(2), 3310-3337.
  • 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.
  • Michiels, F. and De Schepper, A. (2013). A new graphical tool for copula selection. Journal of Computational and Graphical Statistics, 22(2), 471-493.
  • Pickands, J. (1981). Multivariate extreme value distribution. In Proceedings of the International Statistical Institute, 859-878.
  • Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges. Publications de lInstitut de Statistique de lUniversite de Paris, 8, 229-231.
  • 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.

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

Yıl 2022, Cilt: 14 Sayı: 2, 38 - 50, 31.12.2022

Öz

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.

Kaynakça

  • 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.
  • Brechmann, E.C. (2013). Properties of extreme-value copulas. [Thesis, Technical University of Munich].
  • Capéraà, P., Fougres, A.L. and Genest, C. (1997). A nonparametric estimation procedure for bivariate extreme value copulas. Biometrika, 84, 567-577.
  • Durante, F., Fernández-Sánchez, J. and Pappad´a, R. (2015). Copulas, diagonals and tail dependence. Fuzzy Sets and Systems, 264, 22-41.
  • 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.
  • Frees, E. and Valdez, E. (1998). Understanding relationships using copulas. North American Actuarial Journal, 2, 1-25.
  • Galambos, J. (1975). Order statistics of samples from multivariate distributions. Journal of the American Statistical Association, 70, 674-680.
  • Genest, C., Kojadinovic, I., Néslehová, J. and Yan, J. (2011). A goodness-of-fit test for bivariate extremevalue copulas. Bernoulli, 17(1), 253-275.
  • Genest, C. and Segers, J. (2009). Rank-Based inference for bivariate extreme value copulas. The Annals of Statistics, 37, 2990-3022.
  • Gudendorf, G. and Segers, J. (2011). Nonparametric estimation of an extreme-value copula in arbitrary dimensions. Journal of Multivariate Analysis, 102(1), 37-47.
  • Guillotte, S. and Perron, F. (2016). Polynomial pickands functions. Bernoulli, 22(1), 213-241.
  • 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.
  • Hougaard, P. (1986). A class of multivariate failure time distributions. Biometrika, 73, 671-678.
  • Husler, J. (1986). Extreme values of non-stationary random sequences. Journal of Applied Probability, 23, 937-950.
  • Joe, H. (1990). Multivariate concordance. Journal of Multivariate Analysis, 35, 12-30.
  • Marcon, G., Padoan, S.A. and Antoniano-Villalobos, I. (2016). Bayesian inference for the extremal dependence. Electronic Journal of Statistics, 10(2), 3310-3337.
  • 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.
  • Michiels, F. and De Schepper, A. (2013). A new graphical tool for copula selection. Journal of Computational and Graphical Statistics, 22(2), 471-493.
  • Pickands, J. (1981). Multivariate extreme value distribution. In Proceedings of the International Statistical Institute, 859-878.
  • Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges. Publications de lInstitut de Statistique de lUniversite de Paris, 8, 229-231.
  • 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.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Selim Orhun Susam

Yayımlanma Tarihi 31 Aralık 2022
Kabul Tarihi 16 Eylül 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 14 Sayı: 2

Kaynak Göster

APA Susam, S. O. (2022). A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function. Istatistik Journal of The Turkish Statistical Association, 14(2), 38-50.
AMA Susam SO. A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function. IJTSA. Aralık 2022;14(2):38-50.
Chicago Susam, Selim Orhun. “A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function”. Istatistik Journal of The Turkish Statistical Association 14, sy. 2 (Aralık 2022): 38-50.
EndNote Susam SO (01 Aralık 2022) A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function. Istatistik Journal of The Turkish Statistical Association 14 2 38–50.
IEEE S. O. Susam, “A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function”, IJTSA, c. 14, sy. 2, ss. 38–50, 2022.
ISNAD Susam, Selim Orhun. “A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function”. Istatistik Journal of The Turkish Statistical Association 14/2 (Aralık 2022), 38-50.
JAMA Susam SO. A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function. IJTSA. 2022;14:38–50.
MLA Susam, Selim Orhun. “A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function”. Istatistik Journal of The Turkish Statistical Association, c. 14, sy. 2, 2022, ss. 38-50.
Vancouver Susam SO. A Graphical Tool for Extreme Value Copula Selection Based on the Pickands Dependence Function. IJTSA. 2022;14(2):38-50.