Concentration bounds for the extremal variogram

11/01/2021

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by   Sebastian Engelke, et al.

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In extreme value theory, the extremal variogram is a summary of the tail dependence of a random vector. It is a central ingredient for learning extremal tree structures (arXiv:2012.06179) and has close connections to the estimation of Hüsler-Reiss models and extremal graphical models (arXiv:1812.01734). This note presents concentration results for the empirical version of the extremal variogram under general domain of attraction conditions. The results play a role in extending the findings in arXiv:2012.06179 to increasing dimensions. The note is also the first building block for penalized estimation of sparse Hüsler-Reiss graphical models.