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