The Annals of Statistics

Multivariate density estimation under sup-norm loss: Oracle approach, adaptation and independence structure

Oleg Lepski

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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.

Article information

Source
Ann. Statist. Volume 41, Number 2 (2013), 1005-1034.

Dates
First available in Project Euclid: 29 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1369836968

Digital Object Identifier
doi:10.1214/13-AOS1109

Mathematical Reviews number (MathSciNet)
MR3099129

Zentralblatt MATH identifier
06190474

Subjects
Primary: 62G07: Density estimation

Keywords
Density estimation oracle inequality adaptation upper function

Citation

Lepski, Oleg. Multivariate density estimation under sup-norm loss: Oracle approach, adaptation and independence structure. Ann. Statist. 41 (2013), no. 2, 1005--1034. doi:10.1214/13-AOS1109. https://projecteuclid.org/euclid.aos/1369836968.


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