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 × q random matrices, p ≥ q. Assume that for a fixed p × q matrix B and a sequence of constants b n → ∞, the random matrix b n ( X n − B) converges in distribution to Z. Let ψ( X n ) denote the q-vector of singular values of X n . Under these assumptions, the limiting distribution of b n ( ψ( X n ) − 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.