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2004•BernoulliOpen access

Nonparametric independent component analysis

Alexander M. Samarov, Alexandre B. Tsybakov

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Abstract

We consider the problem of nonparametric estimation of a d-dimensional probability density and its `principal directions' in the independent component analysis model. 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 n-consistent and that the corresponding density estimators converge at the optimal rate.

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What this paper is about

We consider the problem of nonparametric estimation of a d-dimensional probability density and its `principal directions' in the independent component analysis model. 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 n-consistent and that the corresponding density estimators converge at the optimal rate.

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Available abstract

We consider the problem of nonparametric estimation of a d-dimensional probability density and its `principal directions' in the independent component analysis model. 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 n-consistent and that the corresponding density estimators converge at the optimal rate.

Key concepts: Mathematics, Estimator, Nonparametric statistics, Principal component analysis, Multivariate kernel density estimation, Density estimation, Applied mathematics, Component (thermodynamics)

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