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On the eigenvectors of large dimensional sample covariance matrices

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  • Silverstein, Jack W.

Abstract

Let {vij}, i, J = 1,2, ..., be i.i.d. random variables, and for each n let Mn = (1/s)VnVnT, where Vn = (vij), i = 1, 2, ..., n, j = 1, 2, ..., s = s(n), and n/s --> y > 0 as n --> [infinity]. Necessary and sufficient conditions are given to establish the convergence in distribution of certain random variables defined by Mn. When E(v114)

Suggested Citation

  • Silverstein, Jack W., 1989. "On the eigenvectors of large dimensional sample covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 1-16, July.
  • Handle: RePEc:eee:jmvana:v:30:y:1989:i:1:p:1-16
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    Cited by:

    1. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(01), pages 158-195, February.
    2. Olivier Ledoit & Sandrine P�ch�, 2009. "Eigenvectors of some large sample covariance matrices ensembles," IEW - Working Papers 407, Institute for Empirical Research in Economics - University of Zurich.
    3. Joel Bun & Jean-Philippe Bouchaud & Marc Potters, 2016. "Cleaning large correlation matrices: tools from random matrix theory," Papers 1610.08104, arXiv.org.
    4. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    5. Ningning Xia & Zhidong Bai, 2015. "Functional CLT of eigenvectors for large sample covariance matrices," Statistical Papers, Springer, vol. 56(1), pages 23-60, February.

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