Title: Small and large subclasses of copulas
Authors: Fabrizio Durante - University of Salento (Italy) [presenting]
Abstract: In statistical inference for dependence models, most of the procedures are usually proved to work for most underlying copulas, up to an exceptional set that is usually considered ``small''. However, it is not always natural what a small subset is in this context. For a given metric space, topology offers a natural way of distinguishing small and big sets through Baire categories, although this concept may sometimes be deceptive. We review some previous results about meager and not-meager (i.e. typical) subclasses of bivariate copulas. Moreover, we determine the topological size of some subsets of multivariate quasi-copulas, with particular emphasis on those subsets that are lattice completion of the set of copulas.