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Some Applications of Watson's Perturbation Approach to Random Matrices

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  • Ruymgaart, Frits H.
  • Yang, Song

Abstract

In this note we draw attention to Watson's (1983) 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.

Suggested Citation

  • Ruymgaart, Frits H. & Yang, Song, 1997. "Some Applications of Watson's Perturbation Approach to Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 48-60, January.
  • Handle: RePEc:eee:jmvana:v:60:y:1997:i:1:p:48-60
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    Cited by:

    1. Mas, André & Menneteau, Ludovic, 2003. "Large and moderate deviations for infinite-dimensional autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 241-260, November.
    2. Mas, André, 2002. "Weak convergence for the covariance operators of a Hilbertian linear process," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 117-135, May.
    3. Rippl, Thomas & Munk, Axel & Sturm, Anja, 2016. "Limit laws of the empirical Wasserstein distance: Gaussian distributions," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 90-109.
    4. Cupidon, J. & Eubank, R. & Gilliam, D. & Ruymgaart, F., 2008. "Some properties of canonical correlations and variates in infinite dimensions," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1083-1104, July.
    5. Munk, A. & Paige, R. & Pang, J. & Patrangenaru, V. & Ruymgaart, F., 2008. "The one- and multi-sample problem for functional data with application to projective shape analysis," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 815-833, May.
    6. Menneteau, Ludovic, 2005. "Some laws of the iterated logarithm in Hilbertian autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 405-425, February.

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