The Annals of Statistics
- Ann. Statist.
- Volume 39, Number 3 (2011), 1608-1632.
Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality
We address the problem of density estimation with -loss by selection of kernel estimators. We develop a selection procedure and derive corresponding -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 -norms of empirical processes developed recently by Goldenshluger and Lepski [Ann. Probab. (2011), to appear].
Ann. Statist. Volume 39, Number 3 (2011), 1608-1632.
First available in Project Euclid: 7 June 2011
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Goldenshluger, Alexander; Lepski, Oleg. Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality. Ann. Statist. 39 (2011), no. 3, 1608--1632. doi:10.1214/11-AOS883. https://projecteuclid.org/euclid.aos/1307452130