Asymptotic expansions for the distributions of statistics based on a correlation matrix
Sadanori Konishi · Canadian Journal of Statistics · 1978
Abstract 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.