On the multivariate Hüsler-Reiss distribution attracting the maxima of elliptical triangular arrays

Statistics and Probability Letters

Volumn 76, Issue 18, 2006, Pages 2027-2035

  Hashorva, Enkelejd ^a,b  

^a Allianz Suisse   (Switzerland)

^b UNIVERSITY OF BERN   (Switzerland)

Author keywords

Gumbel max domain of attraction; Maxima of triangular arrays; Multivariate elliptical distribution; Multivariate H sler Reiss distribution; Weak convergence

Indexed keywords

EID: 33749669006     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2006.05.022     Document Type: Article

References (18)

1. Berman M.S. Sojourns and Extremes of Stochastic Processes (1992), Wadsworth & Brooks/Cole
2. Cambanis S., Huang S., and Simons G. On the theory of elliptically contoured distributions. J. Multivariate Anal. 11 (1981) 368-385
3. Falk M., and Reiss R.-D. On Pickands coordinates in arbitrary dimensions. J. Multivariate Anal. 92 2 (2004) 426-452
4. Falk M., Hüsler J., and Reiss R.-D. Laws of Small Numbers: Extremes and Rare Events. DMV Seminar, second ed. vol. 23 (2004), Birkhäuser, Basel
5. Fang K.-T., Kotz S., and Ng K.-W. Symmetric Multivariate and Related Distributions (1990), Chapman & Hall, London
6. Galambos J. The Asymptotic Theory of Extreme Order Statistics. second ed (1987), Malabar, Krieger
7. de Haan L. On Regular Variation and its Applications to the Weak Convergence of Sample Extremes (1970), Mathematisch Centrum, Amsterdam, Netherlands
8. Hashorva E. Elliptical triangular arrays in the max-domain of attraction of Hüsler-Reiss distribution. Statist. Probab. Lett. 72 2 (2005) 125-135
9. Hashorva E. Extremes of asymptotically spherical and elliptical random vectors. Insurance Math. Econom. 36 3 (2005) 285-302
10. Hashorva, E., 2006. Gaussian approximation of conditional elliptical random vectors. Stochastic Models 17, to appear.
11. Hüsler J., and Reiss R.-D. Maxima of normal random vectors: between independence and complete dependence. Statist. Probab. Lett. 7 (1989) 283-286
12. Kano Y. Consistency property of elliptical probability density functions. J. Multivariate Anal. 51 (1994) 139-147
13. Kotz S., and Nadarajah S. Some extremal type elliptical distributions. Statist. Probab. Lett. 54 2 (2001) 171-182
14. Kotz S., and Nadarajah S. Extreme Value Distributions, Theory and Applications. second ed. (2005), Imperial College Press
15. Leadbetter M.R., Lindgren G., and Rootzén H. Extremes and Related Properties of Random Sequences and Processes (1983), Springer, New York
16. Reiss R.-D. Approximate Distributions of Order Statistics: with Applications to Nonparametric Statistics (1989), Springer, New York
17. Resnick S.I. Extreme Values, Regular Variation and Point Processes (1987), Springer, New York
18. Sibuya M. Bivariate extreme statistics. Ann. Inst. Statist. Math. 11 (1960) 195-210