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Title: The empirical copula process on classes of non-rectangular sets

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Abstract:

The copula of a random vector with unknown marginals can be estimated non-parametrically by the empirical copula, akin to the empirical distribution. However, the asymptotic analysis of the empirical copula is made considerably more involved than that of the empirical distribution by the use of pseudo-observations, involving the marginal empirical distribution functions. In particular, it is still unknown whether the empirical copula evaluated at a non-rectangular set is asymptotically normally distributed. In this work, sufficient conditions under which this is the case are identified. The result is extended to a Donsker theorem for the empirical copula indexed by an infinite collection of non-rectangular sets. Some aspects of the proof involving geometric measure theory will be discussed. Based on ongoing joint work with Axel B眉cher, Johan Segers and Stanislav Volgushev.

Speaker

Micha毛l Lalancette holds a PhD in Statistics (2022) from the University of Toronto, where he was supervised by Stanislav Volgushev and coadvised by Sebastian Engelke (University of Geneva). He was a postdoctoral fellow at the Technical University of Munich before joining UQAM as an assistant professor of Statistics in 2023. He is broadly interested in multivariate extreme value theory, and in dependence modeling through copulas and graphical models.

Meeting ID: 810 3214 4286

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