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Probabilistic Aspects of Multivariate Extremes

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Statistical Extremes and Applications

Part of the book series: NATO ASI Series ((ASIC,volume 131))

Abstract

The probabilistic theory of multivariate extreme values is reviewed, with emphasis on the limiting asymptotic distributions obtained for the extremes of i.i.d. sequences of random vectors.

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References

  • The following list is not intended to cover the subject, and corresponds to the papers that have been cited in our discussion.

    Google Scholar 

  • Balkema, A. and Resnick, S.I. (1977) Max-infinite divisibility, J. App. Probab. 14 309–319

    Article  MathSciNet  MATH  Google Scholar 

  • De Haan, L. and Resnick, S.I. (1977) Limit theory for multivariate sample extremes, Z. Wahrscheinlichkeit. verw. Gebiete 40 317–337

    Article  MATH  Google Scholar 

  • Berman, S.M. (1961/62) Convergence to bivariate limiting extreme value distributions, Ann. Inst. Statist. Math. 13 217–223

    Google Scholar 

  • Fréchet, M. (1951) Sur les tableaux de corrélation dont les marges sont données, Annales de l’Université de Lyon A3, 14 53–77

    Google Scholar 

  • Geffroy, J. (1958/59) Contributions à la théorie des valeurs extrêmes, Publ. Instit. Statist. Univ. Paris, 7–8 37–184

    Google Scholar 

  • Gumbel, E.J. (1960) Distributions des valeurs extrémes en plusieurs dimensions, Publ. Instit. Statist. Univ. Paris 9 171–3

    MathSciNet  MATH  Google Scholar 

  • Sibuya, M. (1960) Bivariate extreme statistics I, Ann. Inst. Statist. Math. 11 195–210

    Article  MathSciNet  MATH  Google Scholar 

  • Pickands, J. III (1980) Multivariate negative exponential and extreme value distributions, Unpublished manuscript, University of Pennsylvania

    Google Scholar 

  • Pickands, J. III (1981) Multivariate extreme value distributions Proceedings 43d Session of the I.S. I. (Buenos Aires) 859–878

    Google Scholar 

  • Marshall A.W. and 01kin I. (1982) Domains of attraction of multivariate extreme value distributions, Annals of Probability 10 168–177

    Article  MathSciNet  Google Scholar 

  • Deheuvels, P. (1978) Caractérisation complète des lois extrémes multivariées et de la convergence des typés extrêmes, Publ. Instit. Statist. Univ. Paris 23, 1–36

    MATH  Google Scholar 

  • Deheuvels, P. (1980) The decomposition of infinite order and extreme multivariate distributions, in: Asymptotic Theory of Statistical Tests and Estimation, I.M. Chakravarti edit., 259–286, Academic Press, New York

    Google Scholar 

  • Deheuvels, P. (1983) Point processes and multivariate extreme values, J. Multivariate Analysis 13 257–271

    Article  MathSciNet  MATH  Google Scholar 

  • Deheuvels, P. (1983) Point processes and multivariate extreme values (II), to be published in Multivariate Analysis V I, P.R. Krishnaiah edit., North Holland, Amsterdam

    Google Scholar 

  • Deheuvels, P. (1980) Some applications of the dependence functions to statistical inference, Coll. Math. J. Bolyai 32, 183–201, North Holland, Amsterdam

    Google Scholar 

  • Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics, Wiley, New York

    MATH  Google Scholar 

  • Tiago de Oliveira J. (1958) Extrema] distributions, Revista da Fac. Ciencias Univ. Lisboa A7 215–227

    Google Scholar 

  • Tiago de Oliveira J. (1975) Bivariate and multivariate extreme value distributions, in: Statistical Distributions in Scientific work, Patil, G.P. and al. edit., Reidel, Dordrecht 355–61

    Google Scholar 

  • Tiago de Oliveira (1980) Bivariate extremes: foundations and Statistics, in: Multivariate Analysis V, P.R. Krishnaiah ed. North Holland, Amsterdam, 349–368

    Google Scholar 

  • Galambos, J. (1975) Order statistics of samples from multivariate distributions, J.A.S.A. 70 674–680

    MathSciNet  MATH  Google Scholar 

  • Davis, R.A. (1982) Limit laws for the maximum and minimum of stationary sequences, Z. Wahrscheinlichkeit. verw. Gebiete 61 31–42

    Article  MATH  Google Scholar 

  • Barnett, V. (1976) The ordering of multivariate data, J. Royal Stat. Soc. A, 139, 318–354

    Article  Google Scholar 

  • David, H. Order Statistics, Wiley, New York

    Google Scholar 

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© 1984 Springer Science+Business Media Dordrecht

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Deheuvels, P. (1984). Probabilistic Aspects of Multivariate Extremes. In: de Oliveira, J.T. (eds) Statistical Extremes and Applications. NATO ASI Series, vol 131. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3069-3_9

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  • DOI: https://doi.org/10.1007/978-94-017-3069-3_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8401-9

  • Online ISBN: 978-94-017-3069-3

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