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June 2011 Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality
Alexander Goldenshluger, Oleg Lepski
Ann. Statist. 39(3): 1608-1632 (June 2011). DOI: 10.1214/11-AOS883

Abstract

We address the problem of density estimation with "$\mathbb{L}_{s}$-loss by selection of kernel estimators. We develop a selection procedure and derive corresponding $\mathbb{L}_{s}$-risk oracle inequalities. It is shown that the proposed selection rule leads to the estimator being minimax adaptive over a scale of the anisotropic Nikol’skii classes. The main technical tools used in our derivations are uniform bounds on the $\mathbb{L}_{s}$-norms of empirical processes developed recently by Goldenshluger and Lepski [Ann. Probab. (2011), to appear].

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Alexander Goldenshluger. Oleg Lepski. "Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality." Ann. Statist. 39 (3) 1608 - 1632, June 2011. https://doi.org/10.1214/11-AOS883

Information

Published: June 2011
First available in Project Euclid: 7 June 2011

zbMATH: 1234.62035
MathSciNet: MR2850214
Digital Object Identifier: 10.1214/11-AOS883

Subjects:
Primary: 62G05, 62G20

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • June 2011
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