KHINCHINE'S THEOREM AND EDGEWORTH APPROXIMATIONS FOR WEIGHTED SUMS
成果类型：
Article
署名作者：
Bobkov, Sergey G.
署名单位：
University of Minnesota System; University of Minnesota Twin Cities; HSE University (National Research University Higher School of Economics)
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/18-AOS1728
发表日期：
2019
页码：
1616-1633
关键词：
摘要：
Let F-n denote the distribution function of the normalized sum of n i.i.d. random variables. In this paper, polynomial rates of approximation of F n by the corrected normal laws are considered in the model where the underlying distribution has a convolution structure. As a basic tool, the convergence part of Khinchine's theorem in metric theory of Diophantine approximations is extended to the class of product characteristic functions.