Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Nonparametric Independent Component Analysis

Auteur(s):

Code(s) de Classification MSC:

• 62G05 Estimation
• 62G20 Asymptotic properties

Résumé: We consider the problem of nonparametric estimation of $d$-dimensional probability density and its principal directions" in the model of Independent Component Analysis. A new method of estimation based on diagonalization of nonparametric estimates of certain matrix functionals of the density is suggested. We show that the proposed estimators of principal directions are $\sqrt{n}$-consistent and that the corresponding density estimators converge at the optimal rate.

Mots Clés: Independent Component Analysis ; nonparametric density estimation ; estimation of functionals ; projection pursuit

Date: 2002-11-14

Prépublication numéro: PMA-774

Postscript file: PMA-774.ps

Pdf file: PMA-774.pdf