Modified Pillai's trace statistics for two high-dimensional sample covariance matrices
Modified Pillai's trace statistics for two high-dimensional sample covariance matrices
复制标题
两个高维样本协方差矩阵的修改 Pillai 迹统计
DOI：
10.1016/j.jspi.2020.01.002
复制
发表时间：
2020-07-01
影响因子：
0.9
通讯作者：
Bai, Zhidong
中科院分区：
文献类型：
--
作者：
Zhang, Qiuyan;Hu, Jiang;Bai, Zhidong
本研究的目的是在一个高维框架下，通过使用修改的Pillai迹统计量来检验两个协方差矩阵的相等性，即，维度和样本大小成比例地变为无穷大。本文引入了两个修正的Pillai迹统计量，并在零假设下得到了它们的渐近分布。所提出的统计量的好处包括：（1）样本大小可以小于维度;（2）所提出的统计量的极限分布是通用的;（3）我们不限制总体协方差矩阵的结构。理论结果是建立在温和的和实际的假设，并证明其性质的数值模拟和真实的数据分析。(C)2020爱思唯尔B.V.保留所有权利。
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. (C) 2020 Elsevier B.V. All rights reserved.