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Biometrika 1997 84(2):327-337; doi:10.1093/biomet/84.2.327
© 1997 by Biometrika Trust
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Asymptotics of eigenprojections of correlation matrices with some applications in principal components analysis

JAMES R. SCHOTT

Department of Statistics, University of Central Florida Orlando, Florida 32816-2370, U.S.A. e-mail: jschott{at}pegasus.cc.ucf.edu

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.

Key Words: Principal component subapace • Rank of asymptotic covariance matrix


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