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April 2013 Multivariate density estimation under sup-norm loss: Oracle approach, adaptation and independence structure
Oleg Lepski
Ann. Statist. 41(2): 1005-1034 (April 2013). DOI: 10.1214/13-AOS1109

Abstract

This paper deals with the density estimation on $\mathbb{R}^{d}$ under sup-norm loss. We provide a fully data-driven estimation procedure and establish for it a so-called sup-norm oracle inequality. The proposed estimator allows us to take into account not only approximation properties of the underlying density, but eventual independence structure as well. Our results contain, as a particular case, the complete solution of the bandwidth selection problem in the multivariate density model. Usefulness of the developed approach is illustrated by application to adaptive estimation over anisotropic Nikolskii classes.

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Oleg Lepski. "Multivariate density estimation under sup-norm loss: Oracle approach, adaptation and independence structure." Ann. Statist. 41 (2) 1005 - 1034, April 2013. https://doi.org/10.1214/13-AOS1109

Information

Published: April 2013
First available in Project Euclid: 29 May 2013

zbMATH: 1360.62158
MathSciNet: MR3099129
Digital Object Identifier: 10.1214/13-AOS1109

Subjects:
Primary: 62G07

Keywords: Adaptation , Density estimation , Oracle inequality , upper function

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 2 • April 2013
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