Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality

Alexander Goldenshluger; Oleg Lepski

doi:10.1214/11-AOS883

Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality

Alexander Goldenshluger, Oleg Lepski

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We address the problem of density estimation with double-struck L _s-loss by selection of kernel estimators. We develop a selection procedure and derive corresponding double-struck 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 double-struck L_s-norms of empirical processes developed recently by Goldenshluger and Lepski [Ann. Probab. (2011), to appear].

Original language	English
Pages (from-to)	1608-1632
Number of pages	25
Journal	Annals of Statistics
Volume	39
Issue number	3
DOIs	https://doi.org/10.1214/11-AOS883
State	Published - Jun 2011

Keywords

Adaptive estimation
Density estimation
Double-struck L-risk
Empirical process
Kernel estimators
Oracle inequalities

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality

Abstract

Keywords

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