Aggregation of density estimators and dimension reduction.
Alexander Samarov and Alexandre Tsybakov
Advances in Statistical Modeling and Inference. Essays in Honor of
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.