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Bayesian estimation of bivariate Pickands dependence function

Yıl 2022, Cilt: 51 Sayı: 6, 1723 - 1735, 01.12.2022
https://doi.org/10.15672/hujms.682730

Öz

In the present study, Bayesian method of estimating the Pickands dependence function of bivariate extreme-value copulas is proposed. Initially, cubic B-spline regression is used to model the dependence function. Then, the estimator of Pickands dependence function is obtained by the Bayesian approach. Through the estimation process, the prior and the posterior distributions of the parameter vectors are provided. The posterior sampling algorithm is presented in order to approximate the posterior distribution. We give a simulation study to measure and compare the performance of the proposed Bayesian estimator of the Pickands dependence function. A real data example is also illustrated.

Kaynakça

  • [1] A. Ahmadabadi and B. Hudaverdi Ucer, Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach, Comput. Statist. 32 (4), 1515–1532, 2017.
  • [2] C.B. Barber, D.P. Dobkin and H.T. Huhdanpaa, The Quickhull algorithm for convex hulls, ACM Trans. Math. Software 22 (4), 469–483, 1996.
  • [3] B. Bergahus, A. Bücher and H. Dette, Minimum distance estimation of Pickands dependence function for multivariate distributions, Working Paper, 2012.
  • [4] S.P. Brooks, Bayesian computation: a statistical revolution, Philos. Trans. Royal Soc. A 361 (1813), 2681–2697, 2003.
  • [5] A. Bücher, H. Dette and S. Volgushev, New estimators of the Pickands dependence function and a test for extreme-value dependence, Ann. Statist. 39 (4), 1963–2006, 2011.
  • [6] P. Capéraà, A.-L.Fougeres and C. Genest, A nonparametric estimation procedure for bivariate extreme value copulas, Biometrika 84 (4), 567–577, 1997.
  • [7] E. Cormiér, C. Genest and J.G. Neslehova, Using B-splines for nonparametric inference on bivariate extreme-value copulas, Extremes 17 (4), 633–659, 2014.
  • [8] P. Deheuvels, On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions, Statist. Probab. Lett. 12 (5), 429–439, 1991.
  • [9] C. Genest and J.Segers, Rank-based inference for bivariate extreme-value copulas, Ann. Statist. 37 (5B), 2990–3022, 2009.
  • [10] G. Gholami, On the Bayesian change-point problem in regression analysis, J. Stat. Theory Appl. 9 (1), 9–27, 2010.
  • [11] P. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika 82 (4), 711–732, 1995.
  • [12] G. Gudendorf and J. Segers, Nonparametric estimation of an extreme-value copula in arbitrary dimensions, J. Multivariate Anal. 102 (1), 37–47, 2011.
  • [13] S. Guillotte and F. Perron, A Bayesian estimator for the dependence function of a bivariate extremevalue distribution, Canad. J. Statist. 36 (3), 83-396, 2008.
  • [14] E.W. Frees and E.A. Valdez, Understanding relationships using copulas, N. Am. Actuar. J. 2 (1), 1–25, 1998.
  • [15] P. Hall and N. Tajvidi, Distribution and dependence-function estimation for bivariate extreme-value distributions, Bernoulli 6 (5), 835–844, 2000.
  • [16] G. Marcon, S.A. Padoan, P. Naveau, P. Muliere and J. Segers, Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials, J. Statist. Plann. Inference 183, 1-17, 2017.
  • [17] J. Pickands, Multivariate extreme value distribution, in: Proceedings of the 43rd Session of the International Statistical Institute, Buenos Aires, Brazil, 859–878, 1981.
  • [18] J. Segers, Non-parametric inference for bivariate extreme-value copulas, in: M. Ahsanullah and S. Kirmani (ed.) Extreme Value Distributions, Nova Science Publishers, 181–203, 1985.
  • [19] A. Zellner, On assessing prior distributions and Bayesian regression analysis with g prior distributions, in: P. Goel and A. Zellner (ed.) Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti. Studies in Bayesian Econometrics. Elsevier, New York, 233-243, 1986.
  • [20] D. Zhang, M.T Wells and L. Peng, Nonparametric estimation of the dependence function for a multivariate extreme value distribution, J. Multivariate Anal. 99, 577–588, 2008.
Yıl 2022, Cilt: 51 Sayı: 6, 1723 - 1735, 01.12.2022
https://doi.org/10.15672/hujms.682730

Öz

Kaynakça

  • [1] A. Ahmadabadi and B. Hudaverdi Ucer, Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach, Comput. Statist. 32 (4), 1515–1532, 2017.
  • [2] C.B. Barber, D.P. Dobkin and H.T. Huhdanpaa, The Quickhull algorithm for convex hulls, ACM Trans. Math. Software 22 (4), 469–483, 1996.
  • [3] B. Bergahus, A. Bücher and H. Dette, Minimum distance estimation of Pickands dependence function for multivariate distributions, Working Paper, 2012.
  • [4] S.P. Brooks, Bayesian computation: a statistical revolution, Philos. Trans. Royal Soc. A 361 (1813), 2681–2697, 2003.
  • [5] A. Bücher, H. Dette and S. Volgushev, New estimators of the Pickands dependence function and a test for extreme-value dependence, Ann. Statist. 39 (4), 1963–2006, 2011.
  • [6] P. Capéraà, A.-L.Fougeres and C. Genest, A nonparametric estimation procedure for bivariate extreme value copulas, Biometrika 84 (4), 567–577, 1997.
  • [7] E. Cormiér, C. Genest and J.G. Neslehova, Using B-splines for nonparametric inference on bivariate extreme-value copulas, Extremes 17 (4), 633–659, 2014.
  • [8] P. Deheuvels, On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions, Statist. Probab. Lett. 12 (5), 429–439, 1991.
  • [9] C. Genest and J.Segers, Rank-based inference for bivariate extreme-value copulas, Ann. Statist. 37 (5B), 2990–3022, 2009.
  • [10] G. Gholami, On the Bayesian change-point problem in regression analysis, J. Stat. Theory Appl. 9 (1), 9–27, 2010.
  • [11] P. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika 82 (4), 711–732, 1995.
  • [12] G. Gudendorf and J. Segers, Nonparametric estimation of an extreme-value copula in arbitrary dimensions, J. Multivariate Anal. 102 (1), 37–47, 2011.
  • [13] S. Guillotte and F. Perron, A Bayesian estimator for the dependence function of a bivariate extremevalue distribution, Canad. J. Statist. 36 (3), 83-396, 2008.
  • [14] E.W. Frees and E.A. Valdez, Understanding relationships using copulas, N. Am. Actuar. J. 2 (1), 1–25, 1998.
  • [15] P. Hall and N. Tajvidi, Distribution and dependence-function estimation for bivariate extreme-value distributions, Bernoulli 6 (5), 835–844, 2000.
  • [16] G. Marcon, S.A. Padoan, P. Naveau, P. Muliere and J. Segers, Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials, J. Statist. Plann. Inference 183, 1-17, 2017.
  • [17] J. Pickands, Multivariate extreme value distribution, in: Proceedings of the 43rd Session of the International Statistical Institute, Buenos Aires, Brazil, 859–878, 1981.
  • [18] J. Segers, Non-parametric inference for bivariate extreme-value copulas, in: M. Ahsanullah and S. Kirmani (ed.) Extreme Value Distributions, Nova Science Publishers, 181–203, 1985.
  • [19] A. Zellner, On assessing prior distributions and Bayesian regression analysis with g prior distributions, in: P. Goel and A. Zellner (ed.) Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti. Studies in Bayesian Econometrics. Elsevier, New York, 233-243, 1986.
  • [20] D. Zhang, M.T Wells and L. Peng, Nonparametric estimation of the dependence function for a multivariate extreme value distribution, J. Multivariate Anal. 99, 577–588, 2008.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm İstatistik
Yazarlar

Alireza Ahmadabadi 0000-0003-0749-4034

Gholamhossein Gholami 0000-0002-2554-2506

Burcu Hudaverdi 0000-0002-6939-9668

Yayımlanma Tarihi 1 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 51 Sayı: 6

Kaynak Göster

APA Ahmadabadi, A., Gholami, G., & Hudaverdi, B. (2022). Bayesian estimation of bivariate Pickands dependence function. Hacettepe Journal of Mathematics and Statistics, 51(6), 1723-1735. https://doi.org/10.15672/hujms.682730
AMA Ahmadabadi A, Gholami G, Hudaverdi B. Bayesian estimation of bivariate Pickands dependence function. Hacettepe Journal of Mathematics and Statistics. Aralık 2022;51(6):1723-1735. doi:10.15672/hujms.682730
Chicago Ahmadabadi, Alireza, Gholamhossein Gholami, ve Burcu Hudaverdi. “Bayesian Estimation of Bivariate Pickands Dependence Function”. Hacettepe Journal of Mathematics and Statistics 51, sy. 6 (Aralık 2022): 1723-35. https://doi.org/10.15672/hujms.682730.
EndNote Ahmadabadi A, Gholami G, Hudaverdi B (01 Aralık 2022) Bayesian estimation of bivariate Pickands dependence function. Hacettepe Journal of Mathematics and Statistics 51 6 1723–1735.
IEEE A. Ahmadabadi, G. Gholami, ve B. Hudaverdi, “Bayesian estimation of bivariate Pickands dependence function”, Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 6, ss. 1723–1735, 2022, doi: 10.15672/hujms.682730.
ISNAD Ahmadabadi, Alireza vd. “Bayesian Estimation of Bivariate Pickands Dependence Function”. Hacettepe Journal of Mathematics and Statistics 51/6 (Aralık 2022), 1723-1735. https://doi.org/10.15672/hujms.682730.
JAMA Ahmadabadi A, Gholami G, Hudaverdi B. Bayesian estimation of bivariate Pickands dependence function. Hacettepe Journal of Mathematics and Statistics. 2022;51:1723–1735.
MLA Ahmadabadi, Alireza vd. “Bayesian Estimation of Bivariate Pickands Dependence Function”. Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 6, 2022, ss. 1723-35, doi:10.15672/hujms.682730.
Vancouver Ahmadabadi A, Gholami G, Hudaverdi B. Bayesian estimation of bivariate Pickands dependence function. Hacettepe Journal of Mathematics and Statistics. 2022;51(6):1723-35.