Fisher information and the central limit theorem

• 成果类型: Article
• 署名作者: Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Goetze, Friedrich
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0500-5
• 发表日期: 2014
• 页码: 1-59
• 关键词: nonuniform bounds

摘要

An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.