Deficiency distance between multinomial and multivariate normal experiments

• 成果类型: Article
• 署名作者: Carter, AV
• 署名单位: University of California System; University of California Santa Barbara
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2002
• 页码: 708-730
• 关键词: asymptotic equivalence; white-noise

摘要

The deficiency distance between a multinomial and a multivariate normal experiment is bounded under a condition that the parameters are bounded away from zero. This result can be used as a key step in establishing asymptotic normal approximations to nonparametric density estimation experiments. The bound relies on the recursive construction of explicit Markov kernels that can be used to reproduce one experiment from the other. The distance is then bounded using classic local-limit bounds between binomial and normal distributions. Some extensions to other appropriate normal experiments are also presented.