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Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices

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  • Silverstein, J. W.
  • Choi, S. I.

Abstract

Results on the analytic behavior of the limiting spectral distribution of matrices of sample covariance type, studied in Marcenko and Pastur [2] and Yin [8], are derived. Through an equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and resembles [formula] for most cases of x0 in the boundary of its support. A complete analysis of a way to determine its support, originally outlined in Marcenko and Pastur [2], is also presented.

Suggested Citation

  • Silverstein, J. W. & Choi, S. I., 1995. "Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 295-309, August.
  • Handle: RePEc:eee:jmvana:v:54:y:1995:i:2:p:295-309
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