In this paper, we study the convergent limits and rates of the eigenvalues and eigenvectors for spiked sample covariance matrices whose spectrum can have multiple bulk components. Our model is an extension of Johnstone’s spiked covariance matrix model. Based on our results, we can extend many statistical applications based on Johnstone’s spiked covariance matrix model.

中文翻译：

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加标样本协方差矩阵可能具有多个批量组件

在本文中，我们研究了光谱可以具有多个体积分量的加标样本协方差矩阵的特征值和特征向量的收敛极限和速率。我们的模型是 Johnstone 的尖峰协方差矩阵模型的扩展。根据我们的结果，我们可以扩展许多基于 Johnstone 的尖峰协方差矩阵模型的统计应用。