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 → ∞, the random matrix bn(Xn − B) converges in distribution to Z. Let ψ(Xn) denote the q-vector of singular values of Xn. Under these assumptions, the limiting distribution of bn (ψ(Xn) − ψ(B)) is characterized as a function of B and of the limit matrix Z. Applications to canonical correlations and to correspondence analysis are given.