  Vine copulas are a useful statistical tool to describe the dependence
structure between several random variables, especially when the number of
variables is very large. When modeling data with vine copulas, one often is
confronted with a set of candidate models out of which the best one is supposed
to be selected. For example, this may arise in the context of non-simplified
vine copulas, truncations of vines and other simplifications regarding
pair-copula families or the vine structure. With the help of distance measures
we develop a parametric bootstrap based testing procedure to decide between
copulas from nested model classes. In addition we use distance measures to
select among different candidate models. All commonly used distance measures,
e.g. the Kullback-Leibler distance, suffer from the curse of dimensionality due
to high-dimensional integrals. As a remedy for this problem, Killiches, Kraus
and Czado (2017) propose several modifications of the Kullback-Leibler
distance. We apply these distance measures to the above mentioned model
selection problems and substantiate their usefulness.
