Dissimilarity functions for copula-based hierarchical clustering of continuous variables
Di Lascio FML
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A copula-based notion of dissimilarity between continuous random variables is introduced and formalized. Such a concept aims at detecting rank--invariant dependence properties among random variables and, as such, it will be defined as a functional on the collection of all copulas. We show how the provided definition includes previous dissimilarity measures considered in the literature like those derived from measures of association and tail dependence but also those of agglomerative hierarchical type. In the latter case, it turns out that the related clustering procedure does not consider the higher-dimensional dependencies among the involved random variables; for instance, they cannot correctly group variables that are pairwise independent but not globally independent. Finally, we compare novel proposed clustering algorithms (taking into account higher-dimensional dependencies) with classical agglomerative clustering methods.