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Asymptotic expansions for the distributions of statistics based on a correlation matrix
Author(s) -
Konishi Sadanori
Publication year - 1978
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314825
Subject(s) - mathematics , principal component analysis , statistic , statistics , asymptotic distribution , v statistic , multivariate normal distribution , covariance matrix , correlation , test statistic , asymptotic expansion , matrix (chemical analysis) , multivariate statistics , mathematical analysis , statistical hypothesis testing , geometry , materials science , estimator , composite material
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.