R-estimation for asymmetric independent component analysis

Independent Component Analysis (ICA) recently has attracted much attention in the statistical literature as an appealing alternative to elliptical models. Whereas k-dimensional elliptical densities depend on one single unspecified radial density, however, k-dimensional independent component distributions involve k unspecified component densities. In practice, for given sample size n and dimension k, this makes the statistical analysis much harder. We focus here on the estimation, from an independent sample, of the mixing/demixing matrix of the model. Traditional methods (FOBI, Kernel-ICA, FastICA) mainly originate from the engineering literature. Their consistency requires moment conditions, they are poorly robust, and do not achieve any type of asymptotic efficiency. When based on robust scatter matrices, the two-scatter methods developed by Oja et al. (2006) and Nordhausen et al. (2008) enjoy better robustness features, but their optimality properties remain unclear. The “classical semiparametric ” approach by Chen and Bickel (2006), quite on the contrary, achieves semiparametric efficiency, but requires the estimation of the densities of the k unobserved independent compo