Nonparametric independent component analysis

Alexander Samarov; Alexandre Tsybakov

doi:10.3150/bj/1093265630

Nonparametric independent component analysis

Alexander Samarov
, Alexandre Tsybakov

Massachusetts Institute of Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	565-582
Number of pages	18
Journal	Bernoulli
Volume	10
Issue number	4
DOIs	https://doi.org/10.3150/bj/1093265630
Publication status	Published - 1 Aug 2004

Keywords

Estimation of functionals
Independent component analysis
Nonparametric density estimation
Projection pursuit

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title = "Nonparametric independent component analysis",

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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author = "Alexander Samarov and Alexandre Tsybakov",

year = "2004",

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AU - Samarov, Alexander

AU - Tsybakov, Alexandre

PY - 2004/8/1

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N2 - 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.

AB - 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.

KW - Estimation of functionals

KW - Independent component analysis

KW - Nonparametric density estimation

KW - Projection pursuit

UR - https://www.scopus.com/pages/publications/29144464874

U2 - 10.3150/bj/1093265630

DO - 10.3150/bj/1093265630

M3 - Article

AN - SCOPUS:29144464874

SN - 1350-7265

VL - 10

SP - 565

EP - 582

JO - Bernoulli

JF - Bernoulli

IS - 4

ER -

Nonparametric independent component analysis

Abstract

Keywords

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