Weak convergence of empirical copula processes indexed by functions
  Weak convergence of the empirical copula process indexed by a class of functions is established. Two scenarios are considered in which either some smoothness of these functions or smoothness of the underlying copula function is required.   A novel integration by parts formula for multivariate, right continuous functions of bounded variation, which is perhaps of independent interest, is proved. It is a key ingredient in proving weak convergence of a general empirical process indexed by functions of bounded variation. 
Dragan Radulovic, Marten Wegkamp, Yue Zhao
math.ST stat.TH