B0619
Title: Multivariate generalized Pareto distributions along extreme directions
Authors: Anas Mourahib - ISBA, UCLouvain (Belgium) [presenting]
Johan Segers - Universite catholique de Louvain (Belgium)
Anna Kiriliouk - University of Namur (Belgium)
Abstract: Consider a random vector representing risk factors and suppose that the interest is in extreme scenarios. The Peaks-over-Thresholds method relies on the property that asymptotically, excesses over a high threshold are distributed according to a multivariate generalized Pareto distribution (MGPD). In the literature, its statistical practice has been discussed only when all risk variables are always large simultaneously. This condition is not realistic for example when the dimension of the random vector is high. To address this point, the case is considered where some risks may be large without all other ones being large as well. Such a group of risks will be called an extreme direction. Extreme directions are interpreted in terms of the angular measure on the one hand and in terms of the MGPD on the other hand. A model is then constructed that allows some groups of risks to constitute an extreme direction. This model can be seen as a smoothed version of the well-known max-linear model in the sense that the complete dependence is replaced in the columns of the matrix representation of the model by a weaker dependence structure. For the latter, two examples are considered: the logistic and the Husler-Reiss model. For these two examples of smoothed max-linear models, simulation algorithms are provided for the associated MGPD and its density is computed with respect to an appropriate dominating measure, which is a sum of Lebesgue measures of various dimensions.
