Fisher information inequalities and the central limit theorem

• 成果类型: Article
• 署名作者: Johnson, O; Barron, A
• 署名单位: University of Cambridge; Yale University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0344-0
• 发表日期: 2004
• 页码: 391-409
• 关键词: entropy

摘要

We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L-2 spaces and Poincare inequalities, to provide a better understanding of the decrease in Fisher information implied by results of Barron and Brown. We show that if the standardized Fisher information ever becomes finite then it converges to zero.