标题： 修正的Pillai轨迹统计量用于两个高维样本协方差矩阵 显示英文标题

标题： Modified Pillai's trace statistics for two high-dimensional sample covariance matrices

摘要： 本研究的目标是通过在高维框架下使用修正的Pillai轨迹统计量来检验两个协方差矩阵的相等性，即维度和样本量成比例地趋于无穷大。 在本文中，我们引入了两种修正的Pillai轨迹统计量，并在零假设下获得了它们的渐近分布。 所提出的统计量的优点包括以下几点：(1) 样本量可以小于维度；(2) 所提出统计量的极限分布是普遍的；(3) 我们不限制总体协方差矩阵的结构。 理论结果是在温和且实际的假设下建立的，并通过模拟和实际数据分析展示了其性质。 显示英文摘要

摘要： 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.