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A note on the convergence rate of the spectral distributions of large random matrices

Author

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  • Bai, Z. D.
  • Miao, Baiqi
  • Tsay, Jhishen

Abstract

In this note we show that the spectral distribution of large dimensional Wigner matrix tends to the semicircular law with a convergence rate of Op(n-1/4). Similar results for sample covariance matrix are also given.

Suggested Citation

  • Bai, Z. D. & Miao, Baiqi & Tsay, Jhishen, 1997. "A note on the convergence rate of the spectral distributions of large random matrices," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 95-101, May.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:1:p:95-101
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    Cited by:

    1. Z. D. Bai & Baiqi Miao & Jhishen Tsay, 1999. "Remarks on the Convergence Rate of the Spectral Distributions of Wigner Matrices," Journal of Theoretical Probability, Springer, vol. 12(2), pages 301-311, April.
    2. S. Chatterjee & A. Bose, 2004. "A New Method for Bounding Rates of Convergence of Empirical Spectral Distributions," Journal of Theoretical Probability, Springer, vol. 17(4), pages 1003-1019, October.
    3. Ningning Xia & Zhidong Bai, 2019. "Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices," Statistical Papers, Springer, vol. 60(3), pages 983-1015, June.

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