The asymptotic distribution of singular-values with applications to canonical correlations and correspondence analysis

Morris L. Eaton, David Tyler

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

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 → ∞, 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.

Original languageAmerican English
Pages (from-to)238-264
Number of pages27
JournalJournal of Multivariate Analysis
Volume50
Issue number2
DOIs
StatePublished - Aug 1994

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Keywords

  • Asymptotic distributions
  • Canonical correlations
  • Correspondence analysis
  • Random matrices
  • Singular values

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