  In the last decade, simplified vine copula models have been an active area of
research. They build a high dimensional probability density from the product of
marginals densities and bivariate copula densities. Besides parametric models,
several approaches to nonparametric estimation of vine copulas have been
proposed. In this article, we extend these approaches and compare them in an
extensive simulation study and a real data application. We identify several
factors driving the relative performance of the estimators. The most important
one is the strength of dependence. No method was found to be uniformly better
than all others. Overall, the kernel estimators performed best, but do worse
than penalized B-spline estimators when there is weak dependence and no tail
dependence.
