论文标题
样品协方差矩阵的非对角线条目的点过程收敛
Point process convergence for the off-diagonal entries of sample covariance matrices
论文作者
论文摘要
我们研究IID随机步行序列的点过程收敛。目的是为这些随机步行的极端得出渐近理论。我们显示了在存在$（2+δ）$ TH时的最大随机步行到Gumbel分布的收敛性。对于IID随机变量的总和，我们大量使用精确的大偏差结果。结果，我们得出了样品协方差和相关矩阵的高维样品的关节收敛，其尺寸随样本量而增加。这将最大入口的渐近态性牙齿属性概括为已知的结果。
We study point process convergence for sequences of iid random walks. The objective is to derive asymptotic theory for the extremes of these random walks. We show convergence of the maximum random walk to the Gumbel distribution under the existence of a $(2+δ)$th moment. We make heavily use of precise large deviation results for sums of iid random variables. As a consequence, we derive the joint convergence of the off-diagonal entries in sample covariance and correlation matrices of a high-dimensional sample whose dimension increases with the sample size. This generalizes known results on the asymptotic Gumbel property of the largest entry.
