An Introduction to Functional Extreme Value Theory
The extension of D-norms to functional spaces in Section 1.10 provides a smooth approach to functional extreme value theory, in particular to generalized Pareto processes and max-stable processes. Multivariate max-stable dfs were introduced in Section 2.3 by means of generalized Pareto distributions. We repeat this approach and introduce max-stable processes via generalized Pareto processes. In Section 4.3, we show how to generate max-stable processes via SMS rvs. This approach, which generalizes the max-linear model established by Wang and Stoev (2011), entails the prediction of max-stable processes in space, not in time. The Brown–Resnick process is a prominent example.
- Dombry, C., and Ribatet, M. (2015). Functional regular variations, Pareto processes and peaks over threshold. In Special Issue on Extreme Theory and Application (Part II) (Y. Wang and Z. Zhang, eds.), Statistics and Its Interface, vol. 8, 9–17. doi:10.4310/SII.2015.v8.n1.a2.MathSciNetCrossRefGoogle Scholar
- Giné, E., Hahn, M., and Vatan, P. (1990). Max-infinitely divisible and max-stable sample continuous processes. Probab. Theory Related Fields 87, 139–165. doi:10.1007/BF01198427.Google Scholar
- de Haan, L., and Ferreira, A. (2006). Extreme Value Theory: An Introduction. Springer Series in Operations Research and Financial Engineering. Springer, New York. doi:10.1007/0-387-34471-3. See http://people.few.eur.nl/ldehaan/EVTbook.correction.pdf and http://home.isa.utl.pt/~anafh/corrections.pdf for corrections and extensions.CrossRefGoogle Scholar