Testing for a multivariate generalized Pareto distribution

Extremes

Volumn 12, Issue 1, 2009, Pages 33-51

  Falk, M ^a   Michel, R ^b  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b Altran CIS GmbH   (Germany)

Author keywords

Excess distribution; Multivariate extreme value distribution; Multivariate generalized Pareto distribution; Peaks over threshold approach; Single sample t test; Threshold selection

Indexed keywords

EID: 59449095575     PISSN: 13861999     EISSN: 1572915X     Source Type: Journal    
DOI: 10.1007/s10687-008-0067-1     Document Type: Article

References (26)

1. A.A. Balkema L. de Haan 1974 Residual life time at great age Ann. Probab. 2 792 804
2. Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J., De Waal, D., Ferro, C.: Statistics of Extremes: Theory and Applications. Wiley, New York (2004)
3. Coles, S.: An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics, Springer, New York (2001)
4. A.C. Davison R.L. Smith 1990 Models for exceedances over high thresholds J. R. Stat. Soc. B 52 393 442
5. Falk, M., Hüsler, J., Reiss, R.-D.: Laws of Small Numbers: Extremes and Rare Events, 2nd edn. Birkhäuser, Basel (2004)
6. M. Falk A. Guillou 2008 Peaks-over-threshold stability of multivariate generalized Pareto distributions J. Multivar. Anal. 99 715 734
7. Fougères, A.-L.: Multivariate extremes. In: Finkenstädt, B., Rootzén, H. (eds.) Extreme Values in Finance, Telecommunications, and the Environment, pp. 373-388. Chapman and Hall, Boca Raton (2004)
8. Galambos, J.: The Asymptotic Theory of Extreme Order Statistics, 2nd edn. Krieger, Malabar (1987)
9. de Haan, L., Ferreira, A.: Extreme Value Theory. An Introduction. Springer, New York (2006)
10. L. de Haan S.I. Resnick 1977 Limit theory for multivariate sample extremes Z. Wahrscheinlichkeitstheor. Verw. Geb. 40 317 337
11. P. Hall 1982 On some simple estimates of an exponent of regular estimation J. R. Stat. Soc. 44 37 42
12. E. Kaufmann R.-D. Reiss 1993 Strong convergence of multivariate point processes of exceedances Ann. Inst. Stat. Math. 45 433 444
13. E. Kaufmann R.-D. Reiss 1995 Approximation rates for multivariate exceedances J. Stat. Plan. Inference 45 235 245
14. Kotz, S., Nadarajah, S.: Extreme Value Distributions. Imperial College Press, London (2000)
15. Michel, R.: Simulation and estimation in multivariate generalized Pareto Models. Ph.D. thesis, University of Würzburg. Available at http://www.opus-bayern.de/uni-wuerzburg/volltexte/2006/1848/pdf/ Simulation-and-Estimation-in-Multivariate-Generalized-Pareto-Models.pdf (2006)
16. J. Pickands III 1975 Statistical inference using extreme order statistics Ann. Stat. 3 119 131
17. Pickands III, J.: Multivariate extreme value distributions. In: Proc. 43th Session ISI (Buenos Aires), pp. 859-878. (1981)
18. Reiss, R.-D.: A Course on Point Processes. Springer, New York (1993)
19. Reiss, R.-D., Thomas, M.: Statistical Analysis of Extreme Values, 3rd edn. Birkhäuser, Basel (2007)
20. Resnick, S.I.: Extreme values, regular variation, and point processes. In: Applied Prob., vol. 4. Springer, New York (1987)
21. Resnick, S.I.: Heavy-Tail Phenomena. Probabilistic and Statistical Modeling. Springer, New York (2007)
22. H. Rootzén N. Tajvidi 2006 Multivariate generalized Pareto distributions Bernoulli 12 917 930
23. Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures, 4rd edn. Chapman&Hall/CRC, Boca Raton (2007)
24. Simonoff, J.S.: Smoothing Methods in Statistics. Springer, New York (1996)
25. A. Stephenson 2003 Simulating Multivariate Extreme Value Distributions of Logistic Type Extremes 6 49 59
26. Tajvidi, N.: Characterization and some statistical aspects of univariate and multivariate generalised Pareto distributions. Ph.D. thesis, Dept. Math., University of Göteborg (1996)