论文标题
修改了两个高维样品协方差矩阵的Pillai的微量统计数据
Modified Pillai's trace statistics for two high-dimensional sample covariance matrices
论文作者
论文摘要
这项研究的目的是通过在高维框架下使用改良的Pillai的痕量统计数据来测试两个协方差矩阵的平等性，即，维度和样本量与无限级相称。在本文中，我们介绍了两个修改后的Pillai的痕量统计数据，并在原假设下获得其渐近分布。提议的统计数据的好处包括：（1）样本量可以小于尺寸； （2）拟议统计数据的限制分布是普遍的； （3）我们不限制种群协方差矩阵的结构。理论结果是在轻度和实用的假设下建立的，并且通过模拟和真实的数据分析来证明它们的特性。
The goal of this study was to test the equality of two covariance matrices by using modified Pillai's trace statistics under a high-dimensional framework, i.e., the dimension and sample sizes go to infinity proportionally. In this paper, we introduce two modified Pillai's trace statistics and obtain their asymptotic distributions under the null hypothesis. The benefits of the proposed statistics include the following: (1) the sample size can be smaller than the dimensions; (2) the limiting distributions of the proposed statistics are universal; and (3) we do not restrict the structure of the population covariance matrices. The theoretical results are established under mild and practical assumptions, and their properties are demonstrated numerically by simulations and a real data analysis.
