  A pair-copula construction is a decomposition of a multivariate copula into a
structured system, called regular vine, of bivariate copulae or pair-copulae.
The standard practice is to model these pair-copulae parametrically, which
comes at the cost of a large model risk, with errors propagating throughout the
vine structure. The empirical pair-copula proposed in the paper provides a
nonparametric alternative still achieving the parametric convergence rate. It
can be used as a basis for inference on dependence measures, for selecting and
pruning the vine structure, and for hypothesis tests concerning the form of the
pair-copulae.
