Topic: Contributed on Asymptotic properties in nonparametric problems Title: Evading the curse of dimensionality in nonparametric density estimation with simplified vines Authors:  Thomas Nagler - Leiden University (Germany) [presenting]
Claudia Czado - Technische Universitaet Muenchen (Germany)
Abstract: Nonparametric density estimators in more than a few dimensions suffer a great deal from the well-known curse of dimensionality: convergence slows down as dimension increases. A result will be presented that shows that the curse of dimensionality can be avoided by assuming a simplified vine copula model for the dependence between variables. In such models, the conditional dependencies are not affected by the values of the conditioning variables. Under mild and general assumptions, corresponding estimators are consistent and the speed of convergence is independent of dimension. Simulation experiments illustrate the large gain in accuracy - even when the true density does not belong to the class of simplified vines.