Some applications of Watson’s perturbation approach to random matrices. (English) Zbl 0927.62018

Summary: We draw attention to G. S. Watson’s [Statistics on spheres. (1983; Zbl 0646.62045)] perturbation approach to random matrices, by which the asymptotic distribution of eigenvalues and eigenvectors can be derived in a very elegant way. We extend his result to functions of matrices and give some applications in principal component analysis, multivariate analysis, and canonical correlations. \(\copyright\) Academic Press.


62E20 Asymptotic distribution theory in statistics
62H25 Factor analysis and principal components; correspondence analysis
62H99 Multivariate analysis
15B52 Random matrices (algebraic aspects)
62H10 Multivariate distribution of statistics


Zbl 0646.62045
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