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Title: On weak conditional convergence of bivariate Archimedean and extreme value copulas Authors:  Thimo Kasper - University of Salzburg (Austria) [presenting]
Sebastian Fuchs - University of Salzburg (Austria)
Wolfgang Trutschnig - University of Salzburg (Austria)
Abstract: Looking at bivariate copulas from the perspective of conditional distributions and considering the weak convergence of almost all conditional distributions yields the notion of weak conditional convergence. At first glance, this notion of convergence for copulas might seem far too restrictive to be of any practical importance - in fact, given samples of a copula $C$ the corresponding empirical copulas do not converge weakly conditional to $C$ with probability one in general. Within the class of Archimedean copulas and the class of Extreme Value copulas, however, standard pointwise convergence and weak conditional convergence can even be proved to be equivalent. Moreover, it can be shown that every copula $C$ is the weak conditional limit of a sequence of checkerboard copulas. After proving these three main results and pointing out some consequences some implications for two recently introduced dependence measures and for the nonparametric estimation of Archimedean and Extreme Value copulas are sketched.