Penalized maximum likelihood and semiparametric second-order efficiency

• 成果类型: Article
• 署名作者: Dalalyan, AS; Golubev, GK; Tsybakov, AB
• 署名单位: Sorbonne Universite; Aix-Marseille Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000895
• 发表日期: 2006
• 页码: 169-201
• 关键词: Adaptive Estimation; models

摘要

We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically efficient and second-order efficient in our model. These estimators are of a penalized maximum likelihood type with an appropriately chosen penalty. We argue that second-order efficiency is crucial in semiparametric problems since only the second-order terms in asymptotic expansion for the risk account for the behavior of the nonparametric component of a semiparametric procedure, and they are not dramatically smaller than the first-order terms.