Independent Component Analysis by Wavelets

Pascal Barbedor (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We propose an ICA contrast based on the density estimation of the observed signal and its marginals by means of wavelets. The risk of the associated moment estimator is linked with approximation properties in Besov spaces. It is shown to converge faster than the at least expected minimax rate carried over from the underlying density estimations. Numerical simulations performed on some common types of densities yield very competitive results, with a high sensitivity to small departures from independence.

Mots clés: ICA; wavelets; Besov spaces; nonparametric density estimation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Pascal Barbedor. Independent Component Analysis by Wavelets. Test Publication, 2009, 18, pp.136-155. ⟨10.1007/s11749-007-0073-7⟩. ⟨hal-00005736v2⟩