论文标题
随机矩阵理论的统计应用：两个人群III的比较
Statistical applications of Random matrix theory: comparison of two populations III
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，以确定显着差异。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性质进行足够精确的描述。在本文中，我们将ARXIV：2002.12741扩展为订单$ 1 $和ARXIV的扰动：2002.12703研究更简单的统计数据。研究了第一篇论文中引入的残留尖峰，并导致统计量导致对两个人群的平等测试。模拟表明，这种新测试不依赖于证明和第二篇论文所必需的一些假设。
This paper investigates a statistical procedure for testing the equality of two independently 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 significant differences. To avoid false rejections we must guard against residual spikes and need a sufficiently precise description of the properties of the largest eigenvalues under the null hypothesis. In this paper, we extend arXiv:2002.12741 for perturbation of order $1$ and arXiv:2002.12703 studying simpler statistic. The residual spike introduce in the first paper is investigated and leads to a statistic that results in a good test of equality of two populations. Simulations show that this new test does not rely on some hypotheses that were necessary for the proofs and in the second paper.
