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Original Articles

Estimating the limit distribution of multivariate extremes

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Pages 275-309 | Received 25 Nov 1991, Accepted 24 Jan 1993, Published online: 21 Mar 2007

References

  • Adler , R. “ The Geometry of Random Fields ” . Wiley .
  • Balkema , A. and Resnick , S. 1977 . Max-infinite divisibility . J. Appl. Probab. , 14 : 309 – 319 .
  • Davis , R. and Resnick , S. 1984 . Tail estimates motivated by extreme value theory . Ann. Statist. , 12 : 1467 – 1487 .
  • Haan , L. de . “ Large quantile estimation in a multivariate setting ” . submitted
  • Haan , L. de and Resnick , S. 1977 . Limit theory for multidimensional sample extremes . Z. Wahrscheinlichkeitstheorie verw , 40 : 317 – 337 .
  • Deheuvels , P. and Oliveira , J. Tiago de . 1989 . On the non-parametric estimation of the bivariate extreme value distributions . Statist and Prob. Letters , 8 : 315 – 323 .
  • Dekkers , A. and Haan , L. de . “ Optimal choice of sample function in extreme value theory ” . submitted
  • Dekkers , A. , Einmahl , J. and Haan , L. de . 1989 . A moment estimator for the index of an extreme-value distribution . Ann. Statist. , 17 : 1833 – 1899 .
  • Einmahl , J. 1987 . Multivariate empirical processes . CWI Tract 32 , 17
  • Einmahl , J. 1992 . The a.s. behavior of the weighted empirical process and the L.I.L. for the weighted tail empirical process . Ann. Probability , 17 To appear
  • Einmahl , J. , Haan , L. de and Xin , Huang . “ Estimating a multidimensional extreme-value distribution ” . Submitted
  • Geluk , J. and de Haan , L. 1987 . Regular Variation, Extensions and Tauberian Theorems . CWI Tract 40 , 17
  • Resnick , S. 1986 . Point processes, regular variation and weak convergence . Adv. Appl. Probab. , 18 : 66 – 138 .
  • Resnick , S. “ Extreme Values, Regular Variation, and Point Processes ” . Springer .
  • Resnick , S. and Greenwood , P. 1979 . A bivariate stable characterization and domains of attraction . J. Multivariate Analysis , 9 : 206 – 221 .
  • Serfling , R. J. “ Approximation Theorems of Mathematical Statistics ” . Wiley .
  • Smirnov , N. V. “ Limit distributions for the terms of a variational series ” . American Math. Soc. Translation Series
  • Smith , R. , Tawn , J. and Yuen , S. “ Statistics of multivariate extremes ” . Preprint
  • Straf , M. Weak convergence of stochastic processes with several parameters . Proceedings of the 6th Berkeley Symposium on Math. Stat, and Prob . pp. 187 – 221 .
  • Tawn , J. 1988 . Bivariate extreme value theory:Models and estimation , 75 : 397 – 415 .
  • Vervaat , W. 1972 . Functional central limit theorems for processes with positive drift and their inverses . Z. Wahrscheinlichkeitstheorey verw , 23 : 249 – 253 .

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