NORMAL APPROXIMATION FOR WEIGHTED SUMS UNDER A SECOND-ORDER CORRELATION CONDITION

• 成果类型: Article
• 署名作者: Bobkov, S. G.; Chistyakov, G. P.; Goetze, 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: 10.1214/19-AOP1388
• 发表日期: 2020
• 页码: 1202-1219
• 关键词: CENTRAL-LIMIT-THEOREM; linear functionals; distributions; MARGINALS

摘要

Under correlation-type conditions, we derive an upper bound of order (log n)/n for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures.