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arXiv · 1210.7078

Multivariate density estimation under sup-norm loss: oracle approach, adaptation and independent structure

Lepski Oleg
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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.

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Lepski Oleg. 2012-10-26. Multivariate density estimation under sup-norm loss: oracle approach, adaptation and independent structure. https://arxiv.org/abs/1210.7078

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