论文标题
非脱位随机向量和的高维CLT：$ n^{ - 1/2} $ - rate
High-dimensional CLT for Sums of Non-degenerate Random Vectors: $n^{-1/2}$-rate
论文作者
论文摘要
在本说明中，当随机向量具有非单明的协方差矩阵时，我们为矩形提供了一个浆果 - 矩形。在这种非单词性的假设下，我们证明了浆果的$ n^{ - 1/2} $缩放 - enseen绑定了均值的均值独立随机向量，具有有限的第三刻。证明本质上是组成的方法证明了多元浆果的证据 - 塞纳托夫（Senatov）（2011）的束缚。与其他现有作品类似（Kuchibhotla等人，2018年，Fang和Koike 2020a），该注释考虑了经典CLT证明技术在高维情况下的适用性和有效性。
In this note, we provide a Berry--Esseen bounds for rectangles in high-dimensions when the random vectors have non-singular covariance matrices. Under this assumption of non-singularity, we prove an $n^{-1/2}$ scaling for the Berry--Esseen bound for sums of mean independent random vectors with a finite third moment. The proof is essentially the method of compositions proof of multivariate Berry--Esseen bound from Senatov (2011). Similar to other existing works (Kuchibhotla et al. 2018, Fang and Koike 2020a), this note considers the applicability and effectiveness of classical CLT proof techniques for the high-dimensional case.
