PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Aggregation of density estimators and dimension reduction.
Alexander Samarov and Alexandre Tsybakov
Advances in Statistical Modeling and Inference. Essays in Honor of pp. 233-251, 2007. ISSN ISBN 978-981-270-369-9


We consider the problem of model-selection-type aggregation of arbitrary density estimators using MISE risk. Given a collection of arbitrary density estimators, we propose a data-based selector of the best estimator in the collection and prove a general ready-to-use oracle inequality for the selected aggregate estimator. We then apply this inequality to the adaptive estimation of a multivariate density in a ``multiple index" model. We show that the proposed aggregate estimator adapts to the unknown index space of unknown dimension in the sense that it allows to estimate the density with the optimal rate attainable when the index space is known.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:3858
Deposited By:Alexandre Tsybakov
Deposited On:25 February 2008