Extremal t processes: Elliptical domain of attraction and a spectral representation

Journal of Multivariate Analysis

Volumn 122, Issue , 2013, Pages 409-413

  Opitz, T ^a  

^a UNIVERSITÉ DE MONTPELLIER   (France)

Author keywords

Elliptical distribution; Extremal t process; Max stable process; Spectral construction

Indexed keywords

EID: 84884287605     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2013.08.008     Document Type: Article

References (24)

1. Anderson T.W., Fang K.T. On the theory of multivariate elliptically contoured distributions and their applications. Statistical Inference in Elliptically Contoured and Related Distributions 1990, 1-24. Allerton Press, New York.
2. Beirlant J., Goegebeur Y., Segers J., Teugels J. Statistics of Extremes: Theory and Applications 2004, John Wiley & Sons, New York.
3. Brown B.M., Resnick S.I. Extreme values of independent stochastic processes. J. Appl. Prob. 1977, 732-739.
4. Davis R.A., Mikosch T. Extreme value theory for space-time processes with heavy-tailed distributions. Stochastic Process. Appl. 2008, 118:560-584.
5. Davison A.C., Padoan S., Ribatet M. Statistical modelling of spatial extremes. Statist. Sci. 2012, 27:161-186.
6. de Haan L. A spectral representation for max-stable processes. Ann. Probab. 1984, 12:1194-1204.
7. de Haan L., Ferreira A. Extreme Value Theory: An Introduction 2006, Springer, Berlin.
8. Demarta S., McNeil A.J. The t copula and related copulas. Int. Stat. Rev. 2005, 73:111-129.
9. C. Dombry, F. Éyi-Minko, Regular conditional distributions of max infinitely divisible processes, Arxiv preprint, 2011. arxiv:1109.6492.
10. Dombry C., Éyi-Minko F., Ribatet M. Conditional simulation of max-stable processes. Biometrika 2013, 100:111-124.
11. Falk M., Hüsler J., Reiss R.D. Laws of Small Numbers: Extremes and Rare Events 2011, Springer, Basel. third ed.
12. Hashorva E. Elliptical triangular arrays in the max-domain of attraction of Hüsler-Reiss distribution. Statist. Probab. Lett. 2005, 72:125-135.
13. Hashorva E. On the regular variation of elliptical random vectors. Statist. Probab. Lett. 2006, 76:1427-1434.
14. Hashorva E., Kabluchko Z., Wübker A. Extremes of independent chi-square random vectors. Extremes 2012, 15:35-42.
15. Hüsler J., Reiss R.D. Maxima of normal random vectors: between independence and complete dependence. Statist. Probab. Lett. 1989, 7:283-286.
16. Hult H., Lindskog F. Multivariate extremes, aggregation and dependence in elliptical distributions. Adv. Appl. Probab. 2002, 34:587-608.
17. Kabluchko Z., Schlather M., De Haan L. Stationary max-stable fields associated to negative definite functions. Ann. Probab. 2009, 37:2042-2065.
18. Klüppelberg C., Kuhn G., Peng L. Estimating the tail dependence function of an elliptical distribution. Bernoulli 2007, 13:229-251.
19. Klüppelberg C., Kuhn G., Peng L. Semi-parametric models for the multivariate tail dependence function-the asymptotically dependent case. Scand. J. Stat. 2008, 35:701-718.
20. Nikoloulopoulos A.K., Joe H., Li H. Extreme value properties of multivariate t copulas. Extremes 2009, 12:129-148.
21. Røislien J., Omre H. T-distributed random fields: a parametric model for heavy-tailed well log data. Math. Geol. 2006, 38:821-849.
22. Schlather M. Models for stationary max-stable random fields. Extremes 2002, 5:33-44.
23. Schlather M., Tawn J.A. A dependence measure for multivariate and spatial extreme values: properties and inference. Biometrika 2003, 90:139-156.
24. Segers J. Max-stable models for multivariate extremes. REVSTAT 2012, 10:61-82.