Optimal rates of convergence in the CLT for quadratic forms

• 成果类型: Article
• 署名作者: Bentkus, V; Gotze, F
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1996
• 页码: 466-490
• 关键词: FUNCTIONALS; expansions

摘要

We prove optimal convergence rates in the central limit theorem for sums in R(k). Assuming a fourth moment, we obtain a Berry-Esseen type bound of O(N-1) for the probability of hitting a ball provided that k greater than or equal to 5. The proof still requires a technical assumption related to the independence of coordinates of sums.