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We consider the problem of multivariate density estimation when the unknown density is assumed to follow a particular form of dimensionality reduction, a noisy independent factor analysis (IFA) model. In this model the data are generated by a number of latent independent components having unknown distributions and are observed in Gaussian noise. We do not assume that either the number of components or the matrix mixing the components are known. We show that the densities of this form can be estimated with a fast rate. Using the mirror averaging aggregation algorithm, we construct a density estimator which achieves a nearly parametric rate , independent of the dimensionality of the data, as the sample size n tends to infinity. This estimator is adaptive to the number of components, their distributions and the mixing matrix. We then apply this density estimator to construct nonparametric plug-in …
The Institute of Mathematical Statistics and the Bernoulli Society
Publication date: 
1 Jan 2010

Umberto Amato, Anestis Antoniadis, Alexander Samarov, Alexandre B Tsybakov

Biblio References: 
Volume: 4 Pages: 707-736
Electronic journal of statistics