Strong convergence of ESD for the generalized sample covariance matrices when p/n→0

Statistics and Probability Letters

Volumn 82, Issue 5, 2012, Pages 894-901

  Bao, Zhigang ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

Limiting spectral distribution; Sample covariance matrix; Stieltjes transform

Indexed keywords

EID: 84857251607     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2012.01.012     Document Type: Article

References (9)

1. Bai Z.D., Silverstein J.W. Spectral analysis of large dimensional random matrices. Mathematics Monograph Series 2 2006, Science Press, Beijing.
2. Bai Z.D., Yin Y.Q. Convergence to the semicircle law. Ann. Prob. 1988, 16:863-875. No. 2.
3. Bai Z.D., Zhang L.X. The limiting spectral distribution of the product of the Wigner matrix and a nonegative definite matrix. J. Multivariate Anal. 2010, 101:1927-1949.
4. EL Karoui, N., On the largest eigenvalue of Wishart matrices with identity covariance when n, p and p/n→∞, 2003, Preprint, arxiv:math.ST/0309355.
5. Girko V.L. Theory of Stochastic Canonical Equations. vols. I, II 2001, Kluwer, Dordrecht.
6. Khorunzhy A.M., Khoruzhenko B.A., Pastur L.A. On asymptotic properties of large random matrices with independent entries. J. Math. Phys. 1996, 37:5033.
7. Marcenko V.A., Pastur L.A. Distribution of eigenvalues for some sets of random matrices. Math. USSR-Sb. 1967, 1:457-483.
8. Shcherbina, M., Central limit theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices, 2011, Preprint, arxiv:1101.3249v1.
9. Wigner E. Characteristic vectors of bordered matrices with infinite dimensions. Ann. Math. 1955, 62:548-564.