  Practical applications of nonparametric density estimators in more than three
dimensions suffer a great deal from the well-known curse of dimensionality:
convergence slows down as dimension increases. We show that one can evade the
curse of dimensionality by assuming a simplified vine copula model for the
dependence between variables. We formulate a general nonparametric estimator
for such a model and show under high-level assumptions that the speed of
convergence is independent of dimension. We further discuss a particular
implementation for which we validate the high-level assumptions and establish
its asymptotic normality. Simulation experiments illustrate a large gain in
finite sample performance when the simplifying assumption is at least
approximately true. But even when it is severely violated, the vine copula
based approach proves advantageous as soon as more than a few variables are
involved. Lastly, we give an application of the estimator to a classification
problem from astrophysics.
