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

M. L. Eaton and D. Tyler

Journal of Multivariate Analysis, 1994, vol. 50, issue 2, 238-264

Abstract: 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.

Date: 1994
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