Estimation of Spiked Eigenvalues in Spiked Models

Random Matrices: Theory and Application

Volumn 1, Issue 2, 2012, Pages

  Bai, Zhidong ^a,b   Ding, X U E ^a,c  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c JILIN UNIVERSITY   (China)

Author keywords

estimation; extreme eigenvalues; Sample covariance matrix; spiked population model

Indexed keywords

EID: 85006595657     PISSN: 20103263     EISSN: 20103271     Source Type: Journal    
DOI: 10.1142/S2010326311500110     Document Type: Article

References (31)

1. T. W. Anderson, An Introduction to Multivariate Statistical Analysis (John Wiley & Sons, Hoboken, NJ, 2003).
2. Z. D. Bai, Methodologies in spectral analysis of large-dimensionalRandom matrices a review, Statist. Sinica. 9 (1999) 611-677.
3. Z. D. Bai and J. W. Silverstein, No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices, Ann. Probab. 26(1) (1998) 316-345.
4. Z. D. Bai and J. W. Silverstein, Exact separation of eigenvalues of large dimensional sample covariance matrices. Ann. Probab. 27(3) (1999) 1536-1555.
5. Z. D. Bai and J. W. Silverstein, CLT for linear spectral statistics of large-dimensional sample covariance matrix. Ann. Probab. 32(1A) (2004) 553-605.
6. Z. D. Bai and J. W. Silverstein, Spectral Analysis of Large DimensionalRandom Matrices, 2nd edn. (Science Press, 2010).
7. Z. D. Bai and J. F. Yao, Limit theorems for sample eigenvalues in a genelized spiked population model, preprint (2010), submitted.
8. Z. D. Bai and J. F. Yao, Central limit theorem for eigenvalues in a spiked population model, Ann. Inst. Henri. Poincare Probab. Statist. 44(3) (2008) 447-474.
9. J. Baik, G. Ben Arous and S. Peche, Phase transition of the largest eigenvalue for non-null complex covariance matrices, Ann. Probab. 33 (2005) 1643-1697.
10. J. Baik and J. W. Silverstein, Eigenvalues of large sample covariance matrices of spiked population models, J. Multivariate Anal. 97 (2006) 1382-1408.
11. A. Buja, T. Hastie and R. Tibshirani, Penalized discriminant analysis, Ann. Statist. 23 (1995) 73-102.
12. R. Horn and C. Johnson, Matrix Analysis (Cambridge Press, 1985).
13. D. Hoyle and M. Rattray, Limiting Form of the Sample Covariance Eigenspectrum in PCA and Kernel PCA, Advances in Neural Information Processing Systems (NIPS), Vol. 16 (2003).
14. K. Johansson, Shape fluctuations andRandom matrices, Commun. Math. Phys. 209 (2000) 437-476.
15. I. M. Johnstone, On the distribution of the largest principal component, Ann. Statist. 29 (2001) 295-327.
16. I. M. Johnstone, and A. Y. Lu, Sparse principal component analysis, to appear in J. Amer. Statist. Assoc.
17. I. T. Jolliffe, Principal Component Analysis, 2nd edn. (Springer, 2002).
18. N. EI Karoui, Recent results about the largest eigenvalue ofRandom covariance matrices and statistical application, Acta Phys. Polon. B 36(9) (2005) 2681-2697.
19. N. EI Karoui, Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices, Ann. Probab. 35(2) (2007) 663-714.
20. L. Laloux, P. Cizeau, M. Potters and J. Bouchaud,Random matrix theory and financial correlations, Int. J. Theor. Appl. Finanace. 3(3) (2000) 391-397.
21. Y. Malevergne and D. Sornette, Collective origin of the coexistance of apparent RMT noise and factors in large sample correlation matrices, preprint, arXiv:condmat/0210115.
22. N. J. Patterson, A. L. Price and D. Reich, Population structure and eigenanalysis, PLoS Genet 2(12): E190 (2006).
23. D. Paul, Asymptotics of sample eigenstructure for a large dimensional spiked covariance model, Statist. Sinica. 17 (2007) 1617-1642.
24. S. Peche, Universality results for largest eigenvalues of some sample covariance matrix ensembles, Probab. Theory Relat. Fields. 143 (2009) 481-516.
25. S. Peche, Universality of local eigenvalue statistics forRandom sample covariance matrices, Ph.D. thesis (Ecole Polytechnique Federale de Lausanne, 2003).
26. V. Plerou, P. Gopikrishnan, B. Rosenow, L. Amaral, T. Guhr and H. Stanley,Random matrix approach to cross correlations in financial data, Phys. Rev. E. 65(6) (2002) 0666126.
27. R. Sear and J. Cuesta, Instabilities in complex mixtures with a large number of components, Phys. Rev. Lett. 91(24) (2003) 245701.
28. A. Soshnikov, A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices, J. Statist. Phys. 108 (2002) 1033-1056.
29. A. Soshnikov, Universality at the edge of the spectrum in WignerRandom matrices, Commun. Math. Phys. 207(3) (1999) 697-733.
30. E. Telatar, Capacity of milti-antenna Gaussian channels, European Trans. Telecommun. 10(6) (1999) 585-595.
31. C. Tracy and H. Widom, On orthogonal and symplectic matrix ensembles, Commun. Math. Phys. 177 (1996) 727-754.