Structural adaptation via Lp-norm oracle inequalities

• 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: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0119-5
• 发表日期: 2009
• 页码: 41-71
• 关键词: rates; CONVERGENCE; regression; bounds

摘要

In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the underlying function. The problem of structural adaptation is stated as the problem of selection from a given collection of estimators. We develop a general selection rule and establish for it global oracle inequalities under arbitrary L-p-losses. These results are applied for adaptive estimation in the additive multi-index model.