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arXiv 1408.0508math.PR
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有界可分解随机向量具有最佳已知速率的多元CLT

A multivariate CLT for bounded decomposable random vectors with the best known rate

Xiao Fang

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12 pages
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摘要：

证明了有界可分解$d$ -维随机向量和在非光滑函数距离上具有显式误差界的多元中心极限定理。分解结构类似于Barnovski，Karoenovski和Rucienovski（1989）的分解结构，并且比Chen和Shao（2004）中考虑的局部依赖结构更一般。误差界的阶数为$d^{\frac{1}{4}} n^{-\frac{1}{2}}$，其中$d$是维数，$n$是被加数。对$d$的依赖性，即$d^{\frac{1}{4}}$，即使对于独立且同分布的随机向量的和也是最好的已知依赖性，并且对$n$的依赖性，即$n^{-\frac{1}{2}}$，是最优的。我们应用我们的主要结果随机图的例子。

英文摘要：

We prove a multivariate central limit theorem with explicit error bound on a non-smooth function distance for sums of bounded decomposable $d$-dimensional random vectors. The decomposition structure is similar to that of Barbour, Karoński and Ruciński (1989) and is more general than the local dependence structure considered in Chen and Shao (2004). The error bound is of the order $d^{\frac{1}{4}} n^{-\frac{1}{2}}$, where $d$ is the dimension and $n$ is the number of summands. The dependence on $d$, namely $d^{\frac{1}{4}}$, is the best known dependence even for sums of independent and identically distributed random vectors, and the dependence on $n$, namely $n^{-\frac{1}{2}}$, is optimal. We apply our main result to a random graph example.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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