BANDWIDTH SELECTION IN KERNEL DENSITY ESTIMATION: ORACLE INEQUALITIES AND ADAPTIVE MINIMAX OPTIMALITY
成果类型：
Article
署名作者：
Goldenshluger, Alexander; Lepski, Oleg
署名单位：
University of Haifa; Aix-Marseille Universite
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/11-AOS883
发表日期：
2011
页码：
1608-1632
关键词：
摘要：
We address the problem of density estimation with L(s)(-)loss by selection of kernel estimators. We develop a selection procedure and derive corresponding 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 L-s-norms of empirical processes developed recently by Goldenshluger and Lepski [Ann. Probab. (2011), to appear].