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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
##### Keywords:
perturbation; principal components; robustness
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