Extremal dependence in a Hüsler–Reiss Markov tree

Tree graphical models are suitable for analysing data where variables are naturally connected through a tree graph. Such variables can be found in studying quantities measured on a river: water level, water flow, pollution concentration in the water or the soil nearby the river, etc. In such a model, the joint distribution is completely determined by the tree structure and the bivariate distributions along the edges of the tree. The Hüsler–Reiss model is based on the assumption that the pairwise copula is in the max-domain of attraction of the bivariate one-parameter Hüsler–Reiss copula. We propose estimators of the model parameters and assess their properties theoretically and through Monte Carlo simulations. We also illustrate the estimators on high water levels at the Seine river network near Paris.