RENYI DIVERGENCE AND THE CENTRAL LIMIT THEOREM

• 成果类型: Article
• 署名作者: Bobkov, S. G.; Chistyakov, G. P.; Goerzet, F.
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1261
• 发表日期: 2019
• 页码: 270-323
• 关键词: fisher information; inequalities; entropy; MONOTONICITY; CONVERGENCE; bounds

摘要

We explore properties of the chi(2) and Renyi distances to the normal law and in particular propose necessary and sufficient conditions under which these distances tend to zero in the central limit theorem (with exact rates with respect to the increasing number of summands).