B1489
Title: Morillas type transformations of stable tail dependence functions
Authors: Klaus Herrmann - Université de Sherbrooke (Canada) [presenting]
Marius Hofert - The University of Hong Kong (Hong Kong)
Johanna Neslehova - McGill University (Canada)
Abstract: Stable tail dependence functions play a central role in multivariate extreme value theory as they are linked to the possible dependence structures for multivariate generalized extreme value distributions. Given their importance, it is natural to consider transformations from the set of stable tail dependence functions into itself. One natural candidate for such a transformation is a pre/post-composition construction, where a function is applied to each argument of the stable tail dependence function. To preserve the necessary homogeneity of stable tail dependence functions, an appropriate inverse function is applied as a post-composition to give the final result. A negative result concerning such transformations is discussed by showing that only transformations based on power functions result again in bona fide stable tail dependence functions. This starkly contrasts similar constructions in a copula context studied by a past study. In this case, any n-absolutely monotone surjection from the unit interval into itself is admissible, leaving a wide range of possibilities. The impact of the result is discussed and connections to the more general question of transforming generalized extreme value distributions into generalized extreme value distributions are provided.
