Multivariate Peaks Over Threshold


We already realized in the univariate case that, from the conceptual viewpoint, the peaks-over-threshold method is a bit more complicated than the annual maxima method. One cannot expect that the questions are getting simpler in the multivariate setting. Subsequently, our attention is primarily restricted to the bivariate case, this topic is fully worked out in [16], 2nd ed., for any dimension. A new result about the testing of tail dependence is added in Section 13.3.


Dependence Function Generalize Pareto Distribution Tail Dependence Surge Height Spectral Expansion 
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  1. 2.
    Kaufmann, E. and Reiss, R.-D. (1995). Approximation rates for multivariate exceedances. J. Statist. Plan. Inf. 45, 235–245; see also the DMV Seminar Volume [16].MATHCrossRefGoogle Scholar
  2. 3.
    Tajvidi, N. (1996). Characterization and some statistical aspects of univariate and multivariate generalised Pareto distributions. PhD Thesis, Dept. of Mathematics, University of Göteborg.Google Scholar
  3. 4.
    Huang, X. (1992). Statistics of bivariate extreme values. PhD Thesis, Erasmus University Rotterdam.Google Scholar
  4. 5.
    For further results see Falk, M. and Reiss, R.-D. (2003). Efficient estimators and LAN in canonical bivariate pot models. J. Mult. Analysis 84, 190–207.MATHCrossRefGoogle Scholar
  5. 6.
    Deheuvels, P. (1980). Some applications to the dependence functions in statistical inference: nonparametric estimates of extreme value distributions, and a Kiefer type universal bound for the uniform test of independence. In: Nonparametric Statistical Inference, pp. 183–201, B.V. Gnedenko et al. (eds), North Holland, Amsterdam.Google Scholar
  6. 7.
    Drees, H. and Huang, X. (1998). Best attainable rates of convergence for estimators of the stable tail dependence function. J. Mult. Analysis 64, 25–47.MATHCrossRefGoogle Scholar
  7. 9.
    Ledford, A.W. und Tawn, J.A. (1996). Statistics for near independence in multivariate extreme values. Biometrika 83, 169–187.MATHCrossRefGoogle Scholar
  8. 10.
    Coles, S., Heffernan, J.E. and Tawn, J.A. (1999). Dependence measures for extreme value analyses. Extremes 2, 339–365.MATHCrossRefGoogle Scholar
  9. 11.
    Heffernan, J.E. (2000). A directory of coefficients of tail independence. Extremes 3, 279–290.MATHCrossRefGoogle Scholar
  10. 12.
    Ledford, A.W. und Tawn, J.A. (1997). Modelling dependence within joint tail regions. J.R. Statist. Soc. B 59, 475–499.MATHCrossRefGoogle Scholar
  11. 14.
    Frick, M., Kaufmann, E. and Reiss, R.-D. (2006). Testing the tail-dependence based on the radial component, submitted.Google Scholar
  12. 15.
    Pfanzagl, J. (1974). Allgemeine Methodenlehre der Statistik II. Walter de Gruyter, Berlin.MATHGoogle Scholar

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