Graphical structures in extreme multivariate events

Analysing and estimating the probability of extremes can be quite challenging, especially when the dimension of the problem under study is large. Initially, univariate extreme value models are used for marginal tail estimation and then, the inter-relationships between random variables are captured by modelling the dependence of the extremes. Here, we propose graphical structures in extreme multivariate events of a random vector given that one of its component is large. These structures are motivated by theory and aim to provide better estimates and predictions of extreme quantities of interest as well as to reduce the problems with the curse of dimensionality. The imposition of graphical structures in the estimation of extremes is achieved via simplified parameter structure in maximum likelihood settings and through Monte Carlo simulation from conditional kernel densities. Finally, the increase in efficiency of the estimators and the benefits of the proposed method are illustrated using simulated data and case studies