THE ASYMPTOTIC-DISTRIBUTION OF SINGULAR-VALUES WITH APPLICATIONS TO CANONICAL CORRELATIONS AND CORRESPONDENCE-ANALYSIS

Let X(n), n = 1, 2, ... be a sequence of p x q random matrices, p greater-than-or-equal-to q. Assume that for a fixed p x q matrix B and a sequence of constants b(n) --> infinity, the random matrix b(n)(X(n)-B) converges in distribution to Z. Let psi(X(n)) denote the q-vector of singular values of X(n). Under these assumptions, the limiting distribution of b(n) (psi(X(n)) - psi(B)) is characterized as a function of B and of the limit matrix Z. Applications to canonical correlations and to correspondence analysis are given. (C) 1994 Academic Press, Inc.