@article{FalkFuller2021,
  author    = {Falk, Michael and Fuller, Timo},
  title     = {New characterizations of multivariate Max-domain of attraction and D-Norms},
  series = {Extremes},
  volume    = {24},
  journal   = {Extremes},
  number    = {4},
  issn      = {1572-915X},
  doi       = {10.1007/s10687-021-00416-4},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269071},
  pages     = {849-879},
  year      = {2021},
  abstract  = {In this paper we derive new results on multivariate extremes and D-norms. In particular we establish new characterizations of the multivariate max-domain of attraction property. The limit distribution of certain multivariate exceedances above high thresholds is derived, and the distribution of that generator of a D-norm on R\(^{d}\), whose components sum up to d, is obtained. Finally we introduce exchangeable D-norms and show that the set of exchangeable D-norms is a simplex.},
  language  = {en}
}
@phdthesis{Fuller2020,
  author    = {Fuller, Timo},
  title     = {Contributions to the Multivariate Max-Domain of Attraction},
  doi       = {10.25972/OPUS-20742},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-207422},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {This thesis covers a wide range of results for when a random vector is in the max-domain of attraction of max-stable random vector. It states some new theoretical results in D-norm terminology, but also gives an explaination why most approaches to multivariate extremes are equivalent to this specific approach. Then it covers new methods to deal with high-dimensional extremes, ranging from dimension reduction to exploratory methods and explaining why the Huessler-Reiss model is a powerful parametric model in multivariate extremes on par with the multivariate Gaussian distribution in multivariate regular statistics. It also gives new results for estimating and inferring the multivariate extremal dependence structure, strategies for choosing thresholds and compares the behavior of local and global threshold approaches. The methods are demonstrated in an artifical simulation study, but also on German weather data.},
  subject      = {Extremwertstatistik},
  language  = {en}
}