A0396
Title: Universal copulas
Authors: Gery Geenens - University of New South Wales (Australia) [presenting]
Abstract: Copulas are classically understood as cumulative distribution functions on the unit hypercube with standard uniform margins, referred to as "Sklar's copulas", owing to their central role in the decomposition of multivariate distributions established by the celebrated Sklar's theorem. The argument habitually put forward for outlining the appeal of copula models is that they allow pulling apart the dependence structure of a bivariate vector (the copula) from the individual behaviour of its marginal components. However, this interpretation can only be justified in the continuous framework, as copulas lose their "margin-free" nature outside of it, making Sklar's copula models unfit for modelling dependence between non-continuous variables. It is argued that the notion of copula should not be imprisoned in Sklar's theorem, and an alternative definition of copulas is proposed, which follows from approaching their role and meaning more broadly. This definition coincides with Sklar's copulas in the continuous framework but leads to different concepts in other settings. It is called construction universal copulas, and it is shown that these maintain all the pleasant properties (in particular, 'margin-freeness') that make Sklar's copulas sound and effective in continuous cases. The findings are illustrated with some examples of universal copula modelling between two discrete variables and between one continuous variable and one binary (Bernoulli) variable.
