Extreme dependence models based on event magnitude

Journal of Multivariate Analysis

Volumn 122, Issue , 2013, Pages 1-19

  Padoan, Simone A ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

Cauchy distribution; Extremal coefficient function; Fr chet distribution; H sler Reiss distribution; Max stable processes; Multivariate extremes; Pickands' function; Sea levels; Spatial extremes; Surge levels

Indexed keywords

EID: 84882691073     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2013.07.009     Document Type: Article

References (35)

1. Balkema S.A., Resnick S. Max-infinite divisibility. Journal of Applied Probability 1977, 14:309-319.
2. Blanchet J., Davison A.C. Spatial modelling of extreme snow depth. The Annals of Applied Statistics 2011, 5:1699-1725.
3. Bortot P., Coles S.G., Tawn J.A. The multivariate Gaussian tail model: an application to oceanographic data. Applied Statistics 2000, 49(1):31-49.
4. Brown B.M., Resnick S.I. Extreme values of independent stochastic processes. Journal of Applied Probability 1977, 14:732-739.
5. Buishand T.A. Bivariate extreme-value data and the station-year method. Journal of Hydrology 1984, 69:77-95.
6. Buishand T.A., de Haan L., Zhou C. On spatial extremes: with application to a rainfall problem. The Annals of Applied Statistics 2008, 2(2):624-642.
7. Davison A.C., Gholamrezaee M.M. Geostatistics of extremes. Proceedings of the Royal Society of London 2012, 468:581-608.
8. Davison A.C., Padoan S.A., Ribatet M. Statistical modelling of spatial extremes. Statistical Science (with discussion) 2012.
9. de Haan L., Ferreira A. Extreme Value Theory. An introduction. Springer Series in Operations Research and Financial Engineering 2006, Springer, New York.
10. Falk M., Hüsler J., Reiss R.-D. Laws of Small Numbers: Extremes and Rare Events. DMV Seminar. 2010, 23. Birkhäuser Verlag, Basel. third edition.
11. Fernandez C., Steel M.F.J. Multivariate student-t regression models: pitfalls and inference. Biometrika 1999, 86:153-168.
12. Fisher R.A., Tippett L.H.C. Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proceedings of the Cambridge Philosophical Society 1928, 24:180-190.
13. Gabda D., Towe R., Wadsworth J.L., Tawn J.A. Discussion of the paper statistical modelling of spatial extremes. Statistical Science 2012.
14. Hall P. On the rate of convergence of normal extremes. Journal of Applied Probability 1979, 16(2):433-439.
15. Hashorva E., Kabluchko Z., Wübker A. Extremes of independent chi-square random vectors. Extremes 2010, 15(1):35-42.
16. Hüsler J., Reiss R.-D. Maxima of normal random vectors: between independence and complete dependence. Statistics & Probability Letters 1989, 7(4):283-286.
17. Joe H. Estimation of quantiles of the maximum of n observations. Biometrika 1987, 74(2):347-354.
18. Kabluchko Z., Schlather M. Ergodic properties of max-infinitely divisible processes. Stochastic Processes and their Applications 2010, 120:281-295.
19. Kabluchko Z., Schlather M., de Haan L. Stationary max-stable fields associated to negative definite functions. Annals of Probability 2009, 37(5):2042-2065.
20. Ledford A.W., Tawn J.A. Statistics for near independence in multivariate extreme values. Biometrika 1996, 83:169-187.
21. Ledford A.W., Tawn J.A. Modelling dependence within joint tail regions. Journal of the Royal Statistical Society. Series B 1997, 59:475-499.
22. Lindsay B.G. Composite likelihood methods. Contemporary Mathematics 1988, 80:221-239.
23. Nikoloulopoulos A.K., Joe H., Li H. Extreme value properties of multivariate t copulas. Extremes 2009, 12:129-148.
24. Omey E., Rachev S.T. Rate of convergence in multivariate extreme value theory. Journal of Multivariate Analysis 1991, 38:36-50.
25. Padoan S.A. Multivariate extreme models based on underlying skew-t and skew-normal distributions. Journal of Multivariate Analysis 2011, 102:977-991.
26. Padoan S.A., Ribatet M., Sisson S.A. Likelihood-based inference for max-stable processes. Journal of the American Statistical Association, Theory and Methods 2010, 105(489):263-277.
27. J. Pickands, Multivariate extreme value distributions, in: Proc. 43th Session ISI (Buenos Aires), 1981, pp. 859-878.
28. Resnick S. Extreme Values, Regular Variation, and Point Processes. Applied Probability 1987, 4. Springer-Verlag, New York.
29. Schlather M. Models for stationary max-stable random fields. Extremes 2002, 5:33-44.
30. Smith R.L. Uniform rates of convergence in extreme-value theory. Advances in Applied Probability 1982, 14(3):600-622.
31. Smith R.L. Max-Stable Processes and Spatial Extremes 1990, University of North Carolina.
32. Tawn J.A. Estimating probabilities of extreme sea-levels. Journal of the Royal Statistical Society. Series C 1992, 41(1):77-93.
33. Varin C., Vidoni P. A note on composite likelihood inference and model selection. Biometrika 2005, 92(3):519-528.
34. Varin C., Reid N., Firth D. An overview of composite likelihood methods. Statistica Sinica 2011, 21(1):5-42.
35. Wadsworth J.L., Tawn J.A. Dependence modelling for spatial extremes. Biometrika 2012, 1(1):1-20.