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This article reviews various characterizations of a multivariate extreme dependence function A(·). The most important estimators derived from these characterizations are also sketched. Then, a unifying approach, which puts all these estimators under the same framework, is presented. This unifying approach enables us to construct new estimators and, most importantly, to propose an automatic selection method for an unknown parameter on which all the existing non-parametric estimators of A(·) depend. Constrained smoothing splines and convex hull techniques are used to force the obtained estimators to be extreme dependence functions. A simulation study comparing these estimators on a wide range of extreme dependence functions is provided.

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