论文标题
随机矩阵理论的统计应用：两个人群的比较II
Statistical applications of Random matrix theory: comparison of two populations II
论文作者
论文摘要
本文研究了一个统计程序，用于测试两个独立估计的协方差矩阵的平等，当可能依赖的数据向量的数量较大并且与向量的大小成正比时，即变量的数量。受到随机矩阵理论中使用的尖峰模型的启发，我们集中在矩阵的最大特征值上，以确定显着性。为了避免错误的拒绝，我们必须防止残留的尖峰，并且需要对无原假设下最大特征值的行为进行足够精确的描述。 在本文中，我们提出了一些“不变”定理，使我们能够扩展Arxiv：2002.12741的测试，以使订单$ 1 $扰动到某些订单$ K $的常规测试。本文介绍的统计数据使用户可以基于高维多元数据来测试两个人群的平等。 模拟表明，这些测试比标准多元方法具有更大的检测能力。
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is, the number of variables. Inspired by the spike models used in random matrix theory, we concentrate on the largest eigenvalues of the matrices in order to determine significance. To avoid false rejections we must guard against residual spikes and need a sufficiently precise description of the behaviour of the largest eigenvalues under the null hypothesis. In this paper we propose some "invariant" theorems that allows us to extend the test of arXiv:2002.12741 for perturbation of order $1$ to some general tests for order $k$. The statistics introduced in this paper allow the user to test the equality of two populations based on high-dimensional multivariate data. Simulations show that these tests have more power of detection than standard multivariate approaches.
