Asymptotics of eigenprojections of correlation matrices with some applications in principal components analysis

Abstract

The asymptotic distribution of an eigenprojection for a sample correlation matrix is obtained. In particular, it is shown that the rank of the asymptotic covariance matrix depends on distributional parameters in a somewhat complicated manner. The results obtained in this paper can be used to determine this rank. Some applications of the asymptotic distribution of these eigenprojections to inferential problems involving principal components subspaces are given.