A complement to Le Cam's theorem

• 成果类型: Article
• 署名作者: Low, Mark G.; Zhou, Harrison H.
• 署名单位: University of Pennsylvania; Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000091
• 发表日期: 2007
• 页码: 1146-1165
• 关键词: gaussian white-noise; asymptotic equivalence; DENSITY-ESTIMATION

摘要

This paper examines asymptotic equivalence in the sense of Le Cam between density estimation experiments and the accompanying Poisson experiments. The significance of asymptotic equivalence is that all asymptotically optimal statistical procedures can be carried over from one experiment to the other. The equivalence given here is established under a weak assumption on the parameter space T. In particular, a sharp Besov smoothness condition is given on T which is sufficient for Poissonization, namely, if F is in a Besov ball B-p,q(alpha) (M) with alpha p > 1/2. Examples show Poissonization is not possible whenever up < 1/2. In addition, asymptotic equivalence of the density estimation model and the accompanying Poisson experiment is established for all compact subsets of C([0, 1](m)), a condition which includes all Holder balls with smoothness alpha > 0.