Independent Component Analysis and estimation of a quadratic functional

Details Independent Component Analysis and estimation of a quadratic functional Independent Component Analysis and estimation of a quadratic functional

2006-05-31

arxiv.org/abs/math/0605794v2

Mathematics

Statistics Theory

34 pages

Scientific paper

Independent component analysis (ICA) is linked up with the problem of estimating a non linear functional of a density, for which optimal estimators are well known. The precision of ICA is analyzed from the viewpoint of functional spaces in the wavelet framework. In particular, it is shown that, under Besov smoothness conditions, parametric rate of convergence is achieved by a U-statistic estimator of the wavelet ICA contrast, while the previously introduced plug-in estimator $\hat C^2\_j$, with moderate computational cost, has a rate in $n^{-4s\over 4s+d}$.

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