The Asymptotic Distribution of Singular-Values with Applications to Canonical Correlations and Correspondence Analysis

Let Xn, n = 1, 2, ... be a sequence of p - q random matrices, p >= q. Assume that for a fixed p - q matrix B and a sequence of constants bn --> [infinity], the random matrix bn(Xn - B) converges in distribution to Z. Let [psi](Xn) denote the q-vector of singular values of Xn. Under these assumptions, the limiting distribution of bn ([psi](Xn) - [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.