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Practical applications of nonparametric density estimators in more than threedimensions suffer a great deal from the well-known curse of dimensionality:convergence slows down as dimension increases. We show that one can evade thecurse of dimensionality by assuming a simplified vine copula model for thedependence between variables. We formulate a general nonparametric estimatorfor such a model and show under high-level assumptions that the speed ofconvergence is independent of dimension. We further discuss a particularimplementation for which we validate the high-level assumptions and establishits asymptotic normality. Simulation experiments illustrate a large gain infinite sample performance when the simplifying assumption is at leastapproximately true. But even when it is severely violated, the vine copulabased approach proves advantageous as soon as more than a few variables areinvolved. Lastly, we give an application of the estimator to a classificationproblem from astrophysics.

Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas