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Common principal component subspaces in two groups. (English) Zbl 0638.62057

Summary: 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.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
62E20 Asymptotic distribution theory in statistics
62H15 Hypothesis testing in multivariate analysis
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