Seminar on Probability and Statistics

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Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike

2021/08/18

14:30-16:00   Room # (Graduate School of Math. Sci. Bldg.)
Gery Geenens (The University of New South Wales (UNSW Sydney))
Dependence, Sklar's copulas and discreteness
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Yet the classical copula approach, building on Sklar’s theorem, cannot be legitimised if the variables of interest are not continuous. Indeed in the presence of discreteness, copula models are (i) unidentifiable, and (ii) not margin-free, and this by construction. In spite of the serious inconsistencies that this creates, downplaying statements are widespread in the literature, where copula methods are devised and used in discrete settings. In this work we call to reconsidering this current practice. To reconcile copulas with discreteness, we argued that they should be apprehended from a more fundamental perspective. Inspired by century-old ideas of Yule, we propose a novel construction which allows all the pleasant properties of copulas for modelling dependence (in particular:‘margin-freeness’) to smoothly carry over to the discrete setting.
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLScU9_QHdHZ-JeVyUIJOKUFmYJvG697NBDFkNh735WK9Cov1Og/viewform