On weak conditional convergence of bivariate Archimedean and Extreme Value copulas, and consequences to nonparametric estimation

Looking at bivariate copulas from the perspective of conditional distributions and considering weak convergence almost all yields notion convergence. At first glance, this for might seem far too restrictive to be any practical importance – in fact, given samples a copula C corresponding empirical do not converge weakly with probability one general. Within class Archimedean Extreme Value copulas, however, standard pointwise can even proved equivalent. Moreover, it shown that every is limit sequence checkerboard copulas. After proving these three main results pointing out some consequences, we sketch implications two recently introduced dependence measures nonparametric estimation