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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.

MSC:
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
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