Title: Testing the simplifying assumption in high-dimensional vine copulas,
Abstract: Testing the simplifying assumption in high-dimensional vine copulas is a
difficult task because tests must be based on estimated observations and amount
to checking constraints on high-dimensional distributions. So far,
corresponding tests have been limited to single conditional copulas with a
low-dimensional set of conditioning variables. We propose a novel testing
procedure that is computationally feasible for high-dimensional data sets and
that exhibits a power that decreases only slightly with the dimension. By
discretizing the support of the conditioning variables and incorporating a
penalty in the test statistic, we mitigate the curse of dimensions by looking
for the possibly strongest deviation from the simplifying assumption. The use
of a decision tree renders the test computationally feasible for large
dimensions. We derive the asymptotic distribution of the test and analyze its
finite sample performance in an extensive simulation study. The utility of the
test is demonstrated by its application to 10 data sets with up to 49
dimensions.