Efficient Independent Component Analysis (II)
Independent component analysis (ICA) has been widely used in separating hidden sources from observed linear mixtures in many fields such as brain imaging analysis, signal processing, telecommunication. Many statistical techniques based on M-estimates have been proposed in estimating the mixing matrix. Recently a few methods based on nonparametric tools are also available. However, in-depth analysis on the convergence rate and asymptotic efficiency has not been available. In this paper, we analyze ICA under the framework of semiparametric theory [see Bickel, Klaassen, Ritov and Wellner (1993)] and propose a straightforward estimate based on the efficient score function by using B-spline approximations. This estimate exhibits better performance than standard ICA methods in a variety of simulations. It is proved that this estimator is Fisher efficient under moderate conditions.