On extremal dependence of block vectors

Kybernetika

Volumn 48, Issue 5, 2012, Pages 988-1006

  Ferreira, Helena ^a   Ferreira, Marta ^b  

^a UNIVERSITY OF BEIRA INTERIOR   (Portugal)

^b UNIVERSITY OF MINHO   (Portugal)

Author keywords

Extremal coefficients; Multivariate extreme value theory; Tail dependence

Indexed keywords

EID: 84870779502     PISSN: 00235954     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. J. Beirlant, Y. Goegebeur, J. Segers, and J. Teugels: Statistics of Extremes: Theory and Application. John Wiley, Chichester 2004.
2. S. Coles, J. Heffernan, and J. Tawn: Dependence measures for extreme value analysis. Extremes 2 (1999), 339-366.
3. G. Draisma, H. Drees, A. Ferreira, and L. de Haan: Bivariate tail estimation: dependence in asymptotic independence. Bernoulli 10 (2004), 251-280.
4. H. Drees and P. Müller: Fitting and validation of a bivariate model for large claims. Insurance Math. Econom. 42 (2008), 638-650.
5. P. Embrechts, F. Lindskog, and A. McNeil: Modelling dependence with copulas and applications to risk management. In: Handbook of Heavy Tailed Distibutions in Finance (S. Rachev, ed.), Elsevier, Amsterdam 2003, pp. 329-384.
6. J. D. Fermanian, D. Radulović, and M. Wegkamp: Weak convergence of empirical copula processes. Bernoulli 10 (2004), 5, 847-860.
7. G. Frahm: On the extremal dependence coefficient of multivariate distributions. Statist. Probab. Lett. 76 (2006), 1470-1481.
8. G. Frahm, M. Junker, and R. Schmidt: Estimating the tail-dependence coefficient: properties and pitfalls. Insurance Math. Econom. 37 (2005), 1, 80-100.
9. D. Gilat and T. Hill: One-sided refinements of the strong law of large numbers and the Glivenko-Cantelli theorem. Ann. Probab. 20 (1992), 1213-1221.
10. L. Hua and H. Joe: Tail order and intermediate tail dependence of multivariate copulas. J. Multivariate Anal. 102 (2011), 10, 1454-1471.
11. X. Huang: Statistics of Bivariate Extreme Values. Ph.D. Thesis, Tinbergen Institute Research Series 22, Erasmus University Rotterdam 1992.
12. H. Joe: Multivariate Models and Dependence Concepts. Chapman and Hall, London 1997.
13. A. Krajina: An M-Estimator of Multivariate Tail Dependence. Tilburg University Press 2010.
14. A. Ledford and J. Tawn: Statistics for near independence in multivariate extreme values. Biometrika 83 (1996), 169-187.
15. A. Ledford and J. Tawn: Modelling Dependence within joint tail regions. J. R. Statist. Soc. Ser. B Stat. Methodol. 59 (1997), 475-499.
16. H. Li: Tail Dependence of Multivariate Pareto Distributions. WSU Mathematics Technical Report 2006-6, Washington 2006.
17. H. Li: Tail dependence comparison of survival Marshall-Olkin copulas. Methodol. Comput. Appl. Probab. 10 (2008), 1, 39-54.
18. H. Li: Orthant tail dependence of multivariate extreme value distributions. J. Multivariate Anal. 100 (2009), 1, 243-256.
19. H. Li and Y. Sun: Tail dependence for heavy-tailed scale mixtures of multivariate distributions. J. Appl. Probab. 46 (2009), 4, 925-937.
20. A. W. Marshall and I. Olkin: A multivariate exponential distribution. J. Amer. Statist. Assoc. 62 (1967), 30-44.
21. R. B. Nelsen: Nonparametric measures of multivariate association. In: Distribution with fixed marginals and related topics, IMS Lecture Notes - Monograph Series, Vol. 28 (L. Rüschendorf et al., eds.) Hayward, Institute of Mathematical Statistics 1996, pp. 223-232.
22. R. B. Nelsen: An Introduction to Copulas. Second edition. Springer, New York 2006.
23. G. Neuhaus: On the weak convergence of stochastic processes with multidimensional time parameter. Ann. Math. Statist. 42 (1971), 1285-1295.
24. F. Schmid and R. Schmidt: Multivariate conditional versions of Spearman's rho and related measures of tail dependence. J. Multivariate Anal. 98 (2007), 1123-1140.
25. R. Schmidt and U. Stadtmüller: Nonparametric estimation of tail dependence. Scand. J. Statist. 33 (2006), 307-335.
26. R. L. Smith: Max-stable processes and spatial extremes. Preprint, Univ. North Carolina, USA 1990.
27. R. L. Smith and I. Weissman: Characterization and estimation of the multivariate extremal index. Manuscript, UNC 1996.
28. M. Sibuya: Bivariate extreme statistics. Ann. Inst. Statist. Math. 11 (1960), 195-210.
29. J. Tiago de Oliveira: Structure theory of bivariate extremes: extensions. Est. Mat. Estat. e Econ. 7 (1962/63), 165-195.
30. E. F. Wolff: N-dimensional measures of dependence. Stochastica 4 (1980), 3, 175-188.