AN APPROXIMATE TEST FOR COMMON PRINCIPAL COMPONENT SUBSPACES IN TWO GROUPS

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.