Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions
Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions
复制标题
用异质超几何函数表达奇异 beta F 矩阵的最大特征值
DOI：
10.1142/s2010326322500058
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Hashiguchi Hiroki
中科院分区：
文献类型：
--
作者：
Shimizu Koki;Hashiguchi Hiroki
本文讨论了多元方差分析 (MANOVA) 的奇异随机矩阵最大特征值的精确分布。发展奇异随机矩阵特征值分布理论的关键是使用具有两个矩阵参数的异质超几何函数。在本研究中，我们定义了奇异β矩阵并将非奇异β矩阵的分布扩展到奇异情况。我们还给出了特征值的联合密度和异质超几何函数的最大特征值的精确分布。
In this paper, the exact distribution of the largest eigenvalue of a singular random matrix for multivariate analysis of variance (MANOVA) is discussed. The key to developing the distribution theory of eigenvalues of a singular random matrix is to use heterogeneous hypergeometric functions with two matrix arguments. In this study, we define the singular beta-matrix and extend the distributions of a nonsingular beta-matrix to the singular case. We also give the joint density of eigenvalues and the exact distribution of the largest eigenvalue in terms of heterogeneous hypergeometric functions.