B0761
Title: Max-stable principal component analysis and its properties
Authors: Felix Reinbott - Otto von Guericke University Magdeburg (Germany) [presenting]
Anja Janssen - Otto von Guericke University Magdeburg (Germany)
Martin Schlather - Universitat Mannheim (Germany)
Abstract: Multivariate extreme value theory exhibits a complex dependence structure often described by underlying physical or economic phenomena. This means that observations of data of extremes are often driven by a low-dimensional latent structure. A PCA-like procedure is proposed that allows the approximation of recovery of this hidden causal structure from data by minimizing a suitable distance between the original data and the reconstruction. This approach to PCA for multivariate extremes works with minimal assumptions on the data. It has good statistical properties that preserve the structure of the extreme value distribution for the latent state. Finally, the procedure is demonstrated to be applicable to real datasets up to moderately high dimensions.
