Exact separation of eigenvalues of large dimensional sample covariance matrices

Annals of Probability

Volumn 27, Issue 3, 1999, Pages 1536-1555

  Bai, Z D ^a   Silverstein, Jack W ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Empirical distribution function of eigenvalues; Random matrix; Stieltjes transform

Indexed keywords

EID: 0033164056     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (9)

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3. FAN, K. (1951). Maximum properties and inequalities for the eigenvalues of completely continuous operators. Proc. Nat. Acad. Sci. U.S.A. 37 760-766.
4. HORN, R. A. and JOHNSON, C. R. (1985). Matrix Analysis. Cambridge Univ. Press.
5. MARČENKO, V. A. and PASTUR, L. A. (1967). Distribution of eigenvalues for some sets of random matrices. Math. USSR-Sb. 1 457-483.
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7. SILVERSTEIN, J. W. and CHOI, S. I. (1995). Analysis of the limiting spectral distribution of large dimensional random matrices. J. Multivariate Anal. 54 295-309.
8. SlLVERSTEIN, J. W. and COMBETTES, P. L. (1992). Signal detection via spectral theory of large dimensional random matrices. IEEE Trans. Signal Processing 40 2100-2105.
9. YIN, Y. Q., BAI, Z. D. and KRISHNAIAH, P. R. (1988). On limit of the largest eigenvalue of the large dimensional sample covariance matrix. Probab. Theory Related Fields 78 509-521.