Extensions of subcopulas. (English) Zbl 1373.60037
Summary: In view of Sklar’s Theorem the probability distribution function of every (not necessarily continuous) random vector can be uniquely decomposed in terms of the marginal distributions of its components and a suitable subcopula. The study of such latter functions is therefore of interest for understanding the dependence information of non-continuous variables. Here, we investigate some analytical properties of the class of subcopulas, including compactness (with respect to a novel metric), approximations and Baire category results. Moreover, under a suitable assumption, we describe all possible extensions from a subcopula to a copula in any dimension.
MSC:
| 60E05 | Probability distributions: general theory |
| 60B10 | Convergence of probability measures |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
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