A0923
Title: The empirical copula process on classes of non-rectangular sets
Authors: Axel Buecher - Ruhr-Universitaet Bochum (Germany)
Johan Segers - Universite catholique de Louvain (Belgium)
Stanislav Volgushev - University of Toronto (Canada)
Michael Lalancette - Université du Québec à Montréal (Canada) [presenting]
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. 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.
