Title: Principal component analysis of max-stable distributions
Authors: Felix Reinbott - Otto von Guericke University Magdeburg (Germany) [presenting]
Martin Schlather - Universitat Mannheim (Germany)
Anja Janssen - Otto von Guericke University Magdeburg (Germany)
Abstract: Multivariate extreme value distributions in practice are often driven by few underlying physical or economic phenomena; thus, many applications are interested in recovering a latent structure in the data. We propose a procedure similar to PCA that yields a transformation to a lower dimensional space by minimizing an appropriate distance measure from the reconstruction to the data. This approach to PCA for multivariate extremes allows us to identify possible driving factors behind extreme events and has good statistical properties that preserve the structure of the extreme value distribution for the latent state. Finally, we demonstrate that the procedure is applicable to real datasets up to moderately high dimensions.