A multivariate Berry--Esseen theorem with explicit constants
A multivariate Berry--Esseen theorem with explicit constants
复制标题
具有显式常量的多元Berry--Esseen定理
DOI：
10.3150/18-bej1072
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Martin Raič
中科院分区：
文献类型：
--
作者：
Martin Raič
我们在多元中心极限定理中为独立但不一定是同分布的随机向量之和提供了李雅普诺夫型界。正态近似中的误差是针对某些类别的集合进行估计的，其中包括可测量的凸集类别。误差范围用显式常量表示。利用斯坦因方法证明了这一结果。此外，我们还改进了凸集高斯周长界限中的常数。
We provide a Lyapunov type bound in the multivariate central limit theorem for sums of independent, but not necessarily identically distributed random vectors. The error in the normal approximation is estimated for certain classes of sets, which include the class of measurable convex sets. The error bound is stated with explicit constants. The result is proved by means of Stein's method. In addition, we improve the constant in the bound of the Gaussian perimeter of convex sets.