Extremal t processes: Elliptical domain of attraction and a spectral representation
Abstract
The extremal t process was proposed in the literature for modeling spatial extremes within a copula framework based on the extreme value limit of elliptical t distributions (Davison, Padoan and Ribatet (2012)). A major drawback of this max-stable model was the lack of a spectral representation such that for instance direct simulation was infeasible. The main contribution of this note is to propose such a spectral construction for the extremal t process. Interestingly, the extremal Gaussian process introduced by Schlather (2002) appears as a special case. We further highlight the role of the extremal t process as the maximum attractor for processes with finite-dimensional elliptical distributions. All results naturally also hold within the multivariate domain.
Keywords
Cite
@article{arxiv.1207.2296,
title = {Extremal t processes: Elliptical domain of attraction and a spectral representation},
author = {Thomas Opitz},
journal= {arXiv preprint arXiv:1207.2296},
year = {2013}
}