Robust Nonparametric Copula Based Dependence

A fundamental problem in statistics is the estimation of dependence between random variables. While information theory provides standard measures of dependence (e.g. Shannon-, Rényi-, Tsallis-mutual information (MI)), it is still unknown how to estimate these quantities from i.i.d. samples in the most efficient way. Dependence estimators have numerous applications in real-world problems. Among others, they have been used in feature selection [1], clustering [2], causality detection [3], optimal experimental design [4, 5], fMRI data processing [6], prediction of protein structures [7], boosting, facial expression recognition [8], independent component and subspace analysis [9, 10, 11, 12], and image registration [13, 14, 15]. Density estimation over a high-dimensional domain is known to suffer from the curse of dimension-ality. Therefore, it is of great importance to know which functionals of densities can be estimated efficiently in a direct way, without estimating the density. It has been shown that copula method