Max-stable processes and the functional D-norm revisited
- 90 Downloads
Aulbach et al. (Extremes 16, 255283, 2013) introduced a max-domain of attraction approach for extreme value theory in C[0,1] based on functional distribution functions, which is more general than the approach based on weak convergence in de Haan and Lin (Ann. Probab. 29, 467483, 2001). We characterize this new approach by decomposing a process into its univariate margins and its copula process. In particular, those processes with a polynomial rate of convergence towards a max-stable process are considered. Furthermore we investigate the concept of differentiability in distribution of a max-stable processes.
KeywordsMax-stable process D-norm Functional max-domain of attraction Copula process Generalized Pareto process δ-neighborhood of generalized Pareto process Derivative of D-norm Distributional differentiability
AMS 2000 Subject Classifications60G70
Unable to display preview. Download preview PDF.
- Deheuvels, P.: Probabilistic aspects of multivariate extremes. In: de Oliveira, T.J. (ed.) Statistical Extremes and Applications, pp 117–130 (1984). D. Reidel DordrechtGoogle Scholar
- Dombry, C., Ribatet, M.: Functional regular variations, pareto processes and peaks over threshold type. Tech. Rep. (2013)Google Scholar
- Ferreira, A., de Haan, L.: The generalized Pareto process; with a view towards application and simulation type Tech. Rep. To appear in Bernoulli. arXiv:math.PR1203.2551v2 (2012)
- Galambos, J., 1st: The Asymptotic Theory of Extreme Order Statistics Wiley Series in Probability and Mathematical Statistics. Wiley, New York (1978)Google Scholar
- de Haan, L., Ferreira, A.: Extreme Value Theory: An Introduction Springer Series in Operations Research and Financial Engineering. Springer, New York (2006). See http://people.few.eur.nl/ldehaan/EVTbook.correction.pdf and http://home.isa.utl.pt/anafh/corrections.pdf for corrections and extensionsCrossRefGoogle Scholar