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Biometrika 1988 75(2):229-236; doi:10.1093/biomet/75.2.229
© 1988 by Biometrika Trust
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Common principal component subspaces in two groups

JAMES R. SCHOTT

Department of Statistics, University of Central Florida Orlando, Florida 32816, U.S.A.

One important practical application of principal component analysis is to reduce a large number of variables, say p, to a smaller number, m, by making use of the first m principal components. This technique can easily be extended to two or more groups if the subspaces spanned by the first m principal components are the same for all groups. In this paper we develop an approximate procedure for testing such a hypothesis of common subspaces when two groups are involved. The adequacy of the approximation is investigated by a simulation and the method is illustrated by a numerical example.

Key Words: Common subspace • Dimensionality reduction • Latent root • Latent vector • Principal component analysis


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