论文标题
高维浆果 - 以$ m $依赖的随机样品约束
High-dimensional Berry-Esseen Bound for $m$-Dependent Random Samples
论文作者
论文摘要
在这项工作中，我们提供了一个$（n/m）^{ - 1/2} $ - 对有限的样本贝里 - 埃塞恩（Berry-Esseen）绑定，以$ m $依赖性的高维随机向量在一类超矩形上。这种结合对随机向量（例如非排定协方差和有限的第三矩）的假设最少。该证明使用抗浓缩不平等和浆果之间的电感关系 - 范围，这些界限的灵感来自Chen and Shao（2004）的望远镜方法，以及Kuchibhotla和Rinaldo的递归方法（2020年）。基于关系进行双重诱导，我们获得了依赖样品的紧密浆果 - 埃森边界。
In this work, we provide a $(n/m)^{-1/2}$-rate finite sample Berry-Esseen bound for $m$-dependent high-dimensional random vectors over the class of hyper-rectangles. This bound imposes minimal assumptions on the random vectors such as nondegenerate covariances and finite third moments. The proof uses inductive relationships between anti-concentration inequalities and Berry--Esseen bounds, which are inspired by the telescoping method of Chen and Shao (2004) and the recursion method of Kuchibhotla and Rinaldo (2020). Performing a dual induction based on the relationships, we obtain tight Berry-Esseen bounds for dependent samples.
