论文标题
高维样品自动辅助矩阵的尖刺特征值：CLT和应用
Spiked eigenvalues of high-dimensional sample autocovariance matrices: CLT and applications
论文作者
论文摘要
高维自相应矩阵在缩小尺寸的高维时间序列中起着重要作用。在本文中，我们建立了在一般条件下开发的高维样品自相关矩阵的峰值特征值的中心极限定理（CLT）。尖刺的特征值可以灵活地到达无限的情况下，而无需以差异顺序限制。此外，当尺寸P和时间长度t一起使用无限时，本研究下的峰值特征值的数量和自相关矩阵的时间滞后可能是固定的，也可以趋向于无穷大。作为进一步的统计应用，提出了一项新型的自相应测试，以检测两个高维时间序列的峰值特征值的等效性。说明了各种模拟研究以证明理论发现是合理的。此外，构建了基于自动助力测试的层次聚类方法，并应用于来自多个国家的聚类死亡率数据。
High-dimensional autocovariance matrices play an important role in dimension reduction for high-dimensional time series. In this article, we establish the central limit theorem (CLT) for spiked eigenvalues of high-dimensional sample autocovariance matrices, which are developed under general conditions. The spiked eigenvalues are allowed to go to infinity in a flexible way without restrictions in divergence order. Moreover, the number of spiked eigenvalues and the time lag of the autocovariance matrix under this study could be either fixed or tending to infinity when the dimension p and the time length T go to infinity together. As a further statistical application, a novel autocovariance test is proposed to detect the equivalence of spiked eigenvalues for two high-dimensional time series. Various simulation studies are illustrated to justify the theoretical findings. Furthermore, a hierarchical clustering approach based on the autocovariance test is constructed and applied to clustering mortality data from multiple countries.
