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AN APPROXIMATE TEST FOR COMMON PRINCIPAL

COMPONENT SUBSPACES IN TWO GROUPS

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TERUO FUJIOKA

*Department of Mathematics, Faculty of Science, Hiroshima University, Hiroshima 730, Japan*
(Received March 27, 1990; revised April 27, 1992)

**Abstract.**
Principal component analysis has made an important
contribution to data reduction. In two sample problems, one great interest is
whether we can reduce the number of variables to a smaller number in similar
fashions for both samples. More precisely, we consider the hypothesis
*H*_{m} that the subspaces spanned by the latent vectors of the population
covariance matrices corresponding to the first principal components are the
same in two groups. In this paper, we propose a simple and easily interpreted
test procedure for *H*_{m}.

*Key words and phrases*:
Data reduction, latent root, latent vector,
principal component, conditional Haar distribution.

**Source**
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