On the dependence of the Berry-Esseen bound on dimension
On the dependence of the Berry-Esseen bound on dimension
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DOI：
10.1016/s0378-3758(02)00094-0
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发表时间：
2003-05-01
影响因子：
0.9
通讯作者：
Bentkus, V
中科院分区：
文献类型：
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作者：
Bentkus, V
设X是值在R-d中的随机向量。假设X的均值为零，单位协方差为.写Beta=E\X\(3)。设S-n是X的n个独立副本的归一化和，对Delta(N)=sup(ac为元素)\P{sn是A}-v(A)的一个元素，其中C是R-d的凸子集类，v是标准的d维正态分布，我们证明了Berry-Essea界Delta(N)小于或等于400d(1/4)β/rootn。是否可以去掉d(1/4)或用一个更好的因子(最终是1)来代替，这仍然是一个悬而未决的问题。(C)2002年，爱思唯尔科学公司出版。
Let X be a random vector with values in R-d. Assume that X has mean zero and identity covariance. Write beta = E\X\(3). Let S-n be a normalized sum of n independent copies of X. For Delta(n) = sup(Ais an element ofC) \P{Sn is an element of A} - v(A)\, where C is the class of convex subsets of R-d, and v is the standard d-dimensional normal distribution, we prove a Berry-Esseen bound Delta(n) less than or equal to 400d(1/4) beta/rootn. Whether one can remove or replace the factor d(1/4) by a better one (eventually by 1), remains an open question. (C) 2002 Published by Elsevier Science B.V.