Limiting behavior of eigenvalues in high-dimensional MANOVA via RMT
Limiting behavior of eigenvalues in high-dimensional MANOVA via RMT
复制标题
DOI：
10.1214/17-aos1646
复制
发表时间：
2018-12
期刊：
影响因子：
--
通讯作者：
Z. Bai;K. P. Choi;Y. Fujikoshi
中科院分区：
文献类型：
--
作者：
Z. Bai;K. P. Choi;Y. Fujikoshi
本文给出了高维大样本情况下MANOVA模型和多元判别分析中零值和局部替代情况下特征值的渐近联合分布。我们的结果是由随机矩阵理论（RMT），而不假设正常的人口。值得指出的是，零和非零分布的特征值和不变的检验统计量是渐近稳健的，对偏离正态在高维情况下。指出了多元回归模型中不变检验的零分布的类似性质。文中还给出了RMT中的一些新公式。
In this paper we derive the asymptotic joint distributions of the eigenvalues under the null case and the local alternative cases in the MANOVA model and multiple discriminant analysis when both the dimension and the sample size are large. Our results are obtained by random matrix theory (RMT) without assuming normality in the populations. It is worth pointing out that the null and non-null distributions of the eigenvalues and invariant test statistics are asymptotically robust against departure from normality in high-dimensional situations. Similar properties are pointed out for the null distributions of the invariant tests in multivariate regression model. Some new formulas in RMT are also presented.