Title: Estimating copula density: Convergence speed results
Authors: Jerome Collet - Electricite de France RD Division (France) [presenting]
Abstract: The goal is to estimate the copula density of a $d-$dimensional random variable, without parametric assumptions, using ranks and subsampling. The main feature of this method is a low sensitivity to dimension, on realistic cases. We give a description of the estimation method, a convergence proof, and some hints on convergence speed. In the simple useless case of independence, we prove the convergence speed is the same as for kernel density estimation. In more structured cases, numerical simulations show the impact of dimension is much smaller than for a kernel estimation. Furthermore, we prove that if the underlying model is mainly additive, the impact of dimension is the same as in the parametric case.