An overview of nonparametric tests of extreme-value dependence and of some related statistical procedures

An overview of existing nonparametric tests of extreme-value dependence is presented. Given an i.i.d.\ sample of random vectors from a continuous distribution, such tests aim at assessing whether the underlying unknown copula is of the {\em extreme-value} type or not. The existing approaches available in the literature are summarized according to how departure from extreme-value dependence is assessed. Related statistical procedures useful when modeling data with this type of dependence are briefly described next. Two illustrations on real data sets are then carried out using some of the statistical procedures under consideration implemented in the $\mathsf{\text{R}}$ package {\tt copula}. Finally, the related problem of testing the {\em maximum domain of attraction} condition is discussed.