Title: An essay on copula modelling for discrete random vectors; or how to pour new wine into old bottles
Authors: Gery Geenens - University of New South Wales (Australia) [presenting]
Abstract: Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, ``the fundamental theorem of copulas'', makes a clear distinction between the continuous case and the discrete case, though. In particular, the copula of a discrete random vector is not identifiable, which causes serious inconsistencies. In spite of this, downplaying statements are widespread in the related literature, and copula methods are used for modelling dependence between discrete variables. The soundness of copula modelling for discrete data is called to be reconsidered. A more fundamental construction is suggested which allows copula ideas to smoothly carry over to the discrete case. Actually it is an attempt at rejuvenating some century-old ideas of Udny Yule, who mentioned a similar construction a long time before copulas got in fashion.