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Colored graphical models provide a parsimonious approach to modelinghigh-dimensional data by exploiting symmetries in the model parameters. In thiswork, we introduce the notion of coloring for extremal graphical models onmultivariate Pareto distributions, a natural class of limiting distributionsfor threshold exceedances. Thanks to a stability property of the multivariatePareto distributions, colored extremal tree models can be defined fullynonparametrically. For more general graphs, the parametric family ofH\"usler--Reiss distributions allows for two alternative approaches to coloredgraphical models. We study both model classes and introduce statisticalmethodology for parameter estimation. It turns out that for H\"usler--Reisstree models the different definitions of colored graphical models coincide. Inaddition, we show a general parametric description of extremal conditionalindependence statements for H\"usler--Reiss distributions. Finally, wedemonstrate that our methodology outperforms existing approaches on a real dataset.

Parametric and nonparametric symmetries in graphical models for extremes