摘要
文章研究了高维情形下协方差矩阵的球形检验问题。利用随机矩阵理论,得到了当总体均值未知时经典的U检验统计量在原假设下的渐近分布。数值模拟表明,对于正态或非正态的总体,当均值未知时,修正后的检验统计量对第一类错误有较好的控制,并且与其他检验统计量比较,检验功效显著提高,小样本的情形下效果尤为明显。
This paper studies the sphericity test for high-dimensional covariance matrix. The paper uses stochastic matrix theory to obtain the asymptotic distribution of classical U test statistics under the null hypothesis when the population mean is unknown. Numerical simulation shows that for normal or non-normal populations, when the mean is unknown, the revised test statistics have a better control over the errors of the first type, and the test efficiency is significantly improved compared with other test statistics, especially in the case of small samples.
作者
袁守成
Yuan Shoucheng(School of Mathematics and Statistics,Pu’er University,Pu’er Yunnan 665000,China)
出处
《统计与决策》
CSSCI
北大核心
2021年第7期33-36,共4页
Statistics & Decision
基金
云南省教育厅科学研究基金项目(2018JS516)
普洱学院创新团队项目(K2015042)
关键词
高维协方差矩阵
球形检验
谱分布
检验功效
high-dimensional covariance matrix
sphericity test
spectral distribution
testing power
