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On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
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  • Published: August 1988

On the limit of the largest eigenvalue of the large dimensional sample covariance matrix

  • Y. Q. Yin1 nAff2,
  • Z. D. Bai1 &
  • P. R. Krishnaiah1 

Probability Theory and Related Fields volume 78, pages 509–521 (1988)Cite this article

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  • 207 Citations

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Summary

In this paper the authors show that the largest eigenvalue of the sample covariance matrix tends to a limit under certain conditions when both the number of variables and the sample size tend to infinity. The above result is proved under the mild restriction that the fourth moment of the elements of the sample sums of squares and cross products (SP) matrix exist.

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References

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Author information

Author notes
  1. Y. Q. Yin

    Present address: Department of Mathematics, University of Arizona, 85721, Tucson, AZ, USA

Authors and Affiliations

  1. Center for Multivariate Analysis, Fifth Floor Thackeray Hall, University of Pittsburgh, 15260, Pittsburgh, PA, USA

    Y. Q. Yin, Z. D. Bai & P. R. Krishnaiah

Authors
  1. Y. Q. Yin
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  2. Z. D. Bai
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  3. P. R. Krishnaiah
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Additional information

Research sponsored by the Air Force Office of Scientific Research under Contract F49620-C-0008. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon

The work of this author was done when he was working at the Center for Multivariate Analysis, University of Pittsburgh.

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Yin, Y.Q., Bai, Z.D. & Krishnaiah, P.R. On the limit of the largest eigenvalue of the large dimensional sample covariance matrix. Probab. Th. Rel. Fields 78, 509–521 (1988). https://doi.org/10.1007/BF00353874

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  • Received: 02 May 1985

  • Revised: 21 December 1987

  • Issue Date: August 1988

  • DOI: https://doi.org/10.1007/BF00353874

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Keywords

  • Covariance
  • Covariance Matrix
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
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