On adaptive minimax density estimation on Rd

• 成果类型: Article
• 署名作者: Goldenshluger, A.; Lepski, O.
• 署名单位: University of Haifa; Aix-Marseille Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0512-1
• 发表日期: 2014
• 页码: 479-543
• 关键词: nonlinear estimation

摘要

We address the problem of adaptive minimax density estimation on with -loss on the anisotropic Nikol'skii classes. We fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk. In particular, we show that there are four different regimes with respect to the behavior of the minimax risk. We develop a single estimator which is (nearly) optimal in order over the complete scale of the anisotropic Nikol'skii classes. Our estimation procedure is based on a data-driven selection of an estimator from a fixed family of kernel estimators.