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B0841
Title: Extensions of subcopulas Authors:  Fabrizio Durante - University of Salento (Italy) [presenting]
Abstract: Copulas represent one of the building blocks of modern multivariate analysis since it was shown that the probability law of any random vector can be expressed as a composition of the distribution functions of all one-dimensional margins and a suitable copula. However, while the copula associated with a random vector is unique when the margins are continuous, in the non-continuous case, various copulas can be associated with the same vector, all being coincident in a subset of the copulas domain. This fact poses the natural question of how it is possible to construct a copula given some partial information about the values that it assumes. One of the most common extension procedures is given by the multilinear interpolation (or checkerboard construction), which also plays a central role in characterizing dependence concepts for discrete random vectors. Extension procedures are presented in a high-dimensional framework to transform a specific subcopula to a copula. Moreover, convergence results are given in order to check how these extensions approximate (in different metrics) a given target copula.