论文标题
基于样品平均值和样品协方差矩阵的随机二次形式的CLT
CLT for random quadratic forms based on sample means and sample covariance matrices
论文作者
论文摘要
在本文中，我们使用尺寸还原技术来研究基于样品平均值和样品协方差矩阵的中心极限理论（CLT）随机二次形式。具体来说，我们使用$ u_ {p \ times q} $表示的矩阵，将$ q $ dimensional样本向量映射到$ p $ dimensional子空间，其中$ q \ geq p $或$ q \ gg gg p $。在$ p/n \ rightarrow 0 $的条件下，$（p，n）\ rightarrow \ infty $，我们为样本平均值和样本协方差矩阵获得随机二次表格的CLT。
In this paper, we use the dimensional reduction technique to study the central limit theory (CLT) random quadratic forms based on sample means and sample covariance matrices. Specifically, we use a matrix denoted by $U_{p\times q}$, to map $q$-dimensional sample vectors to a $p$ dimensional subspace, where $q\geq p$ or $q\gg p$. Under the condition of $p/n\rightarrow 0$ as $(p,n)\rightarrow \infty$, we obtain the CLT of random quadratic forms for the sample means and sample covariance matrices.
