Multivariate density estimation under sup-norm loss: oracle approach, adaptation and independent structure
Statistics Theory
2012-10-29 v1 Statistics Theory
Abstract
The paper deals with the density estimation on Rd under sup- norm loss. We provide with fully data-driven estimation procedure and establish for it so called sup-norm oracle inequality. The pro- posed estimator allows to take into account not only approximation properties of the underlying density but eventual independence struc- ture as well. Our results contain, as a particular case, the complete solution of the bandwidth selection problem in multivariate density model. Usefulness of the developed approach is illustrated by appli- cation to adaptive estimation over anisotropic Nikolskii classes.
Keywords
Cite
@article{arxiv.1210.7078,
title = {Multivariate density estimation under sup-norm loss: oracle approach, adaptation and independent structure},
author = {Lepski Oleg},
journal= {arXiv preprint arXiv:1210.7078},
year = {2012}
}