On estimation of the population spectral distribution from a high-dimensional sample covariance matrix

Australian and New Zealand Journal of Statistics

Volumn 52, Issue 4, 2010, Pages 423-437

  Bai, Zhidong ^a   Chen, Jiaqi ^a   Yao, Jianfeng ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITÉ DE RENNES 1   (France)

Author keywords

Eigenvalues of covariance matrices; High dimensional statistics; Mar enko Pastur distribution; Sample covariance matrices

Indexed keywords

EID: 78650655959     PISSN: 13691473     EISSN: 1467842X     Source Type: Journal    
DOI: 10.1111/j.1467-842X.2010.00590.x     Document Type: Article

References (12)

1. Bai, Z.D. & Silverstein, J.W. (2004). CLT for linear spectral statistics of large-dimensional sample covariance matrices. Ann. Probab. 32, 553-605.
2. Bai, Z.D. & Silverstein, J.W. (2006). Spectral Analysis of Large Dimensional Random Matrices. Beijing Science Press.
3. Dempster, A. P. (1958). A high dimensional two sample significance test. Ann. Math. Statist. 29, 995-1010.
4. Dempster, A. P. (1960). A significance test for the separation of two highly multivariate small samples. Biometrics 16, 41-50.
5. El Karoui, N. (2008). Spectrum estimation for large dimensional covariance matrices using random matrix theory. Ann. Statist. 36, 2757-2790.
6. Marćenko, V. & Pastur, L. (1967). Distribution of eigenvalues for some sets of random matrices. Math. USSR-Sb 1, 457-483.
7. Nica, A. & Speicher, R. (2006). Lectures on the Combinatorics of Free Probability. New York Cambridge University Press.
8. Raj Rao, N. (2006). RMTool - A Random Matrix Calculator in MATLAB. Available from URL: .
9. Raj Rao, N., Mingo, J. A., Speicher, R. & Edelman, A. (2008). Statistical eigen-inference from large Wishart matrices. Ann. Statist. 36, 2850-2885.
10. Silverstein, J. W. (1995). Strong convergence of the empirical distribution of eigenvalues of large-dimensional random matrices. J. Multivariate Anal. 55, 331-339.
11. Silverstein, J. W. & Choi, S.-I. (1995). Analysis of the limiting spectral distribution of large-dimensional random matrices. J. Multivariate Anal. 54, 295-309.
12. Szegö, G. (1959). Orthogonal Polynomials. New York American Mathematical Society.