标题： 协方差的同时推断 显示英文标题

标题： Simultaneous Inference of Covariances

摘要： 我们考虑样本协方差矩阵最大偏差的渐近分布，这是协方差高维推断中的基本问题。 在数据矩阵元素的弱依赖条件下，我们建立了最大偏差的Gumbel收敛性。 我们的结果大大推广了早期的研究，这些研究假设元素是独立同分布的，并为协方差的高维同时推断提供了理论基础。 显示英文摘要

摘要： We consider asymptotic distributions of maximum deviations of sample covariance matrices, a fundamental problem in high-dimensional inference of covariances. Under mild dependence conditions on the entries of the data matrices, we establish the Gumbel convergence of the maximum deviations. Our result substantially generalizes earlier ones where the entries are assumed to be independent and identically distributed, and it provides a theoretical foundation for high-dimensional simultaneous inference of covariances.