Multivariate regular variation on cones: Application to extreme values, hidden regular variation and conditioned limit laws

Stochastics

Volumn 80, Issue 2-3, 2008, Pages 269-298

  Resnick, Sidney I ^a  

^a School of Operations Research and Industrial Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 40249095165     PISSN: 17442508     EISSN: 17442516     Source Type: Journal    
DOI: 10.1080/17442500701830423     Document Type: Article

References (26)

1. B. Abdous, A.L. Fougères, and K. Ghoudi, Extreme behaviour for bivariate elliptical distributions, Canad. J. Statist. 33(2) (2005).
2. N. Bingham, C. Goldie, and J. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987.
3. S. Coles, An Introduction to Statistical Modeling of Extreme Values, Springer Series in Statistics, Springer, London, 2001, xiv, p. 210.
4. D. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes. Vol. I: Elementary Theory and Methods, 2nd ed., Vol. xxi, Probability and its Applications Springer, New York, NY, 2003, p. 469.
5. L. de Haan, On Regular Variation and Its Application to the Weak Convergence of Sample Extremes, Mathematisch Centrum, Amsterdam, 1970.
6. L. de Haan and J. de Ronde, Sea and wind: Multivariate extremes at work, Extremes 1(1) (1998), pp. 7-46.
7. L. de Haan and A. Ferreira, Extreme Value Theory: An Introduction, Springer-Verlag, New York, 2006.
8. L. de Haan and S.I. Resnick, Limit theory for multivariate sample extremes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 40(4) (1977), pp. 317-337.
9. P. Embrechts, C. Kluppelberg, and T. Mikosch, Modelling Extreme Events for Insurance and Finance. Springer-Verlag, Berlin, 1997.
10. W. Feller, An Introduction to Probability Theory and Its Applications, 2nd ed., Vol. 2, Wiley, New York, 1971.
11. J.L. Geluk and L. de Haan, Regular Variation, Extensions and Tauberian Theorems, CWI Tract 40, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 1987.
12. J. Heffernan and S. Resnick, Hidden regular variation and the rank transform, Adv. Appl. Prob. 37(2) (2005), pp. 393-414.
13. _, Limit laws for random vectors with an extreme component, Ann. Appl. Probab. 17(2) (2007), pp. 537-571.
14. J. Heffernan and J. Tawn, A conditional approach for multivariate extreme values (with discussion), JRSS B 66(3) (2004), pp. 497-546.
15. O. Kallenberg, Random Measures, 3rd ed., Akademie-Verlag, Berlin, 1983.
16. A. Ledford J. Tawn, Statistics for near independence in multivariate extreme values, Biometrika 83(1) (1996), pp. 169-187.
17. _, Modelling dependence within joint tail regions, J. Roy. Statist. Soc. Ser. B 59(2) (1997), pp. 475-499.
18. A. Marshall and I. Olkin, Domains of attraction of multivariate extreme value distributions, Ann. Probab. 11(1) (1983), pp. 168-177.
19. K. Maulik and S. Resnick, Characterizations and examples of hidden regular variation, Extremes 7(1) (2005), pp. 31-67.
20. J. Neveu, Processus ponctuels, in Proceedings of the École d'Été de Probabilités de Saint-Flour, VI-1976. Springer-Verlag, Berlin, Lecture Notes in Math., Vol. 598, 1977, pp. 249-445.
21. S. Resnick, Extreme Values, Regular Variation and Point Processes. Springer-Verlag, New York, 1987.
22. _, A Probability Path, Birkhäuser, Boston, 1999.
23. _, Hidden regular variation, second order regular variation and asymptotic independence, Extremes 5(4) (2002), pp. 303-336.
24. _, Heavy Tail Phenomena: Probabilistic and Statistical Modeling, Springer Series in Operations Research and Financial Engineering (iSBN: 0-387-24272-4) Springer-Verlag, New York, 2006.
25. E. Seneta, Regularly Varying Functions, Springer-Verlag, New York (lecture Notes in Mathematics, 508) 1976.
26. M. Sibuya, Bivariate extreme statistics, Ann. Inst. Stat. Math. 11 (1960), pp. 195-210.