Consistent independent component analysis and prewhitening

We study the statistical merits of two techniques used in the literature of independent component analysis (ICA). First, we analyze the characteristic-function based ICA method (CHFICA) and study its statistical properties such as consistency, √n-consistency, and robustness against small additive noise. Second, we study the validity of prewhitening: a preprocessing technique used by many ICA algorithms, as applied to the CHFICA method. In particular, we establish the surprising effectiveness of this technique even when some components have heavy tails and others do not. A fast new algorithm implementing the prewhitened CHFICA method is also provided.