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 , 2nd ed., for any dimension. A new result about the testing of tail dependence is added in Section 13.3.
KeywordsDependence Function Generalize Pareto Distribution Tail Dependence Surge Height Spectral Expansion
Unable to display preview. Download preview PDF.
- 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
- 4.Huang, X. (1992). Statistics of bivariate extreme values. PhD Thesis, Erasmus University Rotterdam.Google Scholar
- 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
- 14.Frick, M., Kaufmann, E. and Reiss, R.-D. (2006). Testing the tail-dependence based on the radial component, submitted.Google Scholar