Detecting a conditional extreme value model

Extremes

Volumn 14, Issue 1, 2011, Pages 29-61

  Das, Bikramjit ^a   Resnick, Sidney I ^a  

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

Author keywords

Asymptotic independence; Conditional extreme value model; Domain of attraction; Heavy tails; Regular variation

Indexed keywords

EID: 79952069685     PISSN: 13861999     EISSN: 1572915X     Source Type: Journal    
DOI: 10.1007/s10687-009-0097-3     Document Type: Article

References (30)

1. Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1968).
2. Coles, S. G., Tawn, J. A.: Modelling extreme multivariate events. J. R. Stat. Soc., B 53, 377-392 (1991).
3. Coles, S. G., Heffernan, J. E., Tawn, J. A.: Dependence measures for extreme value analyses. Extremes 2(4), 339-365 (1999).
4. Das, B., Resnick, S. I.: QQ plots, random sets and data from a heavy tailed distribution. Stoch. Models 24(1), 103-132 (2008). ISSN 1532-6349.
5. Das, B., Resnick, S. I.: Conditioning on an extreme component: model consistency and regular variation on cones. http://arxiv.org/abs/0805. 4373 (2009).
6. de Haan, L., de Ronde, J.: Sea and wind: multivariate extremes at work. Extremes 1(1), 7-46 (1998).
7. de Haan, L., Ferreira, A.: Extreme Value Theory: an Introduction. Springer, New York (2006).
8. de Haan, L., Resnick, S. I.: Limit theory for multivariate sample extremes. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 40, 317-337 (1977).
9. Fougères, A., Soulier, P.: Estimation of conditional laws given an extreme component. http://arXiv.org/0806. 2426v2 (2009).
10. Heffernan, J. E., Resnick, S. I.: Limit laws for random vectors with an extreme component. Ann. Appl. Probab. 17(2), 537-571 (2007). ISSN 1050-5164. doi: 10. 1214/105051606000000835.
11. Heffernan, J. E., Tawn, J. A.: A conditional approach for multivariate extreme values (with discussion). JRSS B 66(3), 497-546 (2004).
12. Hill, B. M.: A simple general approach to inference about the tail of a distribution. Ann. Stat. 3, 1163-1174 (1975).
13. Kallenberg, O.: Random Measures, 3rd edn. Akademie-Verlag, Berlin (1983). ISBN 0-12-394960-2.
14. Ledford, A. W., Tawn, J. A.: Statistics for near independence in multivariate extreme values. Biometrika83(1), 169-187 (1996). ISSN 0006-3444.
15. Ledford, A. W., Tawn, J. A.: Modelling dependence within joint tail regions. J. R. Stat. Soc., Ser. B 59(2), 475-499 (1997). ISSN 0035-9246.
16. Ledford, A. W., Tawn, J. A.: Concomitant tail behaviour for extremes. Adv. Appl. Probab. 30(1), 197-215 (1998). ISSN 0001-8678.
17. López-Oliveros, L., Resnick, S. I.: Extremal dependence analysis of network sessions. Extremes (2009). http://arxiv.org/pdf/0905. 1983v1.
18. Mason, D.: Laws of large numbers for sums of extreme values. Ann. Probab. 10, 754-764 (1982).
19. Maulik, K., Resnick, S. I.: Characterizations and examples of hidden regular variation. Extremes 7(1), 31-67 (2005).
20. Maulik, K., Resnick, S. I., Rootzén, H.: Asymptotic independence and a network traffic model. J. Appl. Probab. 39(4), 671-699 (2002). ISSN 0021-9002.
21. McNeil, A. J., Frey, R., Embrechts, P.: Concepts, techniques and tools. In: Quantitative Risk Management. Princeton Series in Finance. Princeton University Press, Princeton (2005). ISBN 0-691-12255-5.
22. Neveu, J.: Processus ponctuels. In: École d'Été de Probabilités de Saint-Flour, VI-1976. Lecture Notes in Math., vol. 598, pp. 249-445. Springer, Berlin (1977).
23. Pickands, J.: Statistical inference using extreme order statistics. Ann. Stat. 3, 119-131 (1975).
24. Resnick, S. I.: A Probability Path. Birkhäuser, Boston (1999).
25. Resnick, S. I.: Hidden regular variation, second order regular variation and asymptotic independence. Extremes 5(4), 303-336 (2002).
26. Resnick. S. I.: Modeling data networks. In: Finkenstadt, B., Rootzén, H. (eds.) SemStat: Seminaire Europeen de Statistique, Extreme Values in Finance, Telecommunications, and the Environment, pp. 287-372. Chapman-Hall, London (2003).
27. Resnick, S. I.: Heavy Tail Phenomena: Probabilistic and Statistical Modeling. Springer Series in Operations Research and Financial Engineering. Springer, New York (2007). ISBN: 0-387-24272-4.
28. Resnick, S. I.: Extreme Values, Regular Variation and Point Processes. Springer Series in Operations Research and Financial Engineering. Springer, New York (2008). ISBN 978-0-387-75952-4. Reprint of the 1987 original.
29. Resnick, S. I., Stǎricǎ, C.: Consistency of Hill's estimator for dependent data. J. Appl. Probab. 32(1), 139-167 (1995). ISSN 0021-9002.
30. Sarvotham, S., Riedi, R., Baraniuk, R.: Network and user driven on-off source model for network traffic. Comput. Networks 48, 335-350 (2005) (Special issue on "Long-range Dependent Traffic").