Asymptotic expansions for the distributions of statistics based on a correlation matrix
Asymptotic expansions for the distributions of statistics based on a correlation matrix
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基于相关矩阵的统计分布的渐近展开
DOI：
10.2307/3314825
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发表时间：
1978
影响因子：
0.6
通讯作者：
S. Konishi
中科院分区：
文献类型：
--
作者：
S. Konishi
当观测值服从多元正态分布时，给出了相关矩阵的α-最大特征根分布的渐近展开式.给出了基于相关矩阵的检验统计量分布的渐近展开式，这对主成分分析中的降维是有用的。当总体相关矩阵的相应特征根是简单的时，这些展开式成立。这里的方法基于扰动方法。
An asymptotic expansion is given for the distribution of the α-th largest latent root of a correlation matrix, when the observations are from a multivariate normal distribution. An asymptotic expansion for the distribution of a test statistic based on a correlation matrix, which is useful in dimensionality reduction in principal component analysis, is also given. These expansions hold when the corresponding latent root of the population correlation matrix is simple. The approach here is based on a perturbation method.