ON THE RATE OF CONVERGENCE IN THE MULTIVARIATE CLT

• 成果类型: Article
• 署名作者: GOTZE, F
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990448
• 发表日期: 1991
• 页码: 724-739
• 关键词: central limit-theorem; statistics

摘要

Berry-Esseen theorems are proved in the multidimensional central limit theorem without using Fourier methods. An effective and simple estimate of the error in the CLT for sums and convex sets using Stein's method and induction is derived. Furthermore, the error in the CLT for multivariate functions of independent random elements is estimated extending results of van Zwet and Friedrich to the multivariate case.