Central Limit Theorem and Diophantine Approximations

被引:8
作者
Bobkov, Sergey G. [1 ]
机构
[1] Univ Minnesota, Sch Math, 127 Vincent Hall,206 Church St SE, Minneapolis, MN 55455 USA
基金
美国国家科学基金会;
关键词
Central limit theorem; Diophantine approximation; Edgeworth expansions;
D O I
10.1007/s10959-017-0770-4
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Let F-n denote the distribution function of the normalized sum Z(n) = (X-1+ ... +X-n)/(sigma root n) of i.i.d. random variables with finite fourth absolute moment. In this paper, polynomial rates of convergence of F-n to the normal law with respect to the Kolmogorov distance, as well as polynomial approximations of F-n by the Edgeworth corrections (modulo logarithmically growing factors in n), are given in terms of the characteristic function of X-1. Particular cases of the problem are discussed in connection with Diophantine approximations.
引用
收藏
页码:2390 / 2411
页数:22
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