Spectral properties of empirical covariance matrices for data with power-law tails

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 4, 2006, Pages

  Burda, Zdzisław ^a   Görlich, Andrzej T ^a   Wacław, Bartłomiej ^a  

^a JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

DATA ACQUISITION; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; SPECTRUM ANALYSIS; STATISTICAL METHODS;

MULTIVARIATE STUDENT DISTRIBUTION; POWER LAW; RANDOM MATRICES; SPECTRAL PROPERTIES;

DATA PROCESSING;

EID: 33750602461     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.041129     Document Type: Article

References (37)

1. T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(97)00088-4 299, 189 (1998).
2. A. L. Moustakas, Science SCIEAS 0036-8075 10.1126/science.287.5451.287 287, 287 (2000).
3. A. M. Sengupta and P. P. Mitra, e-print physics/0010081.
4. R. Müller, IEEE Trans. Inf. Theory IETTAW 0018-9448 48, 2495 (2002).
5. S. E. Skipetrov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.036621 67, 036621 (2003).
6. L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1467 83, 1467 (1999).
7. V. Plerou, P. Gopikrishnan, B. Rosenow, Luis A. Nunes Amaral, T. Guhr, and H. E. Stanley, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.066126 65, 066126 (2002).
8. A. Utsugi, K. Ino, and M. Oshikawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.026110 70, 026110 (2004).
9. S. Pafka and I. Kondor, Physica A PHYADX 0378-4371 319, 487 (2003);
10. S. Pafka and I. Kondor, Physica A PHYADX 0378-4371 343, 623 (2004).
11. G. Papp, S. Pafka, M. A. Nowak, and I. Kondor, Acta Phys. Pol. B APOBBB 0587-4254 36, 2757 (2005).
12. T. Guhr and B. Kälber, J. Phys. A JPHAC5 0305-4470 36, 3009 (2003).
13. Y. Malevergna and D. Sornette, Physica A PHYADX 0378-4371 10.1016/j.physa.2003.09.004 331, 660 (2004).
14. Z. Burda and J. Jurkiewicz, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.06.089 344, 67 (2004).
15. V. A. Marčenko and L. A. Pastur, Math. USSR. Sb. ZZZZZZ 0025-5734 1, 457 (1967).
16. Z. D. Bai and J. W. Silverstein, J. Multivariate Anal. JMVAAI 0047-259X 54, 175 (1995).
17. S. I. Choi and J. W. Silverstein, J. Multivariate Anal. JMVAAI 0047-259X 10.1006/jmva.1995.1058 54, 295 (1995).
18. Z. Burda, J. Jurkiewicz, and B. Wacław, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.026111 71, 026111 (2005).
19. J. Feinberg and A. Zee, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02181233 87, 473 (1997).
20. A. M. Sengupta and P. P. Mitra, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.3389 60, 3389 (1999).
21. Z. Burda, A. Görlich, A. Jarosz, and J. Jurkiewicz, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.05.048 343, 295 (2004).
22. P. Repetowicz and P. Richmond, e-print math-ph/0411020.
23. P. Cizeau, J. P. Bouchaud, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.50.1810 50, 1810 (1994).
24. P. Gopikrishnan, M. Meyer, L. A. Nunes Amaral, and H. E. Stanley, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050292 3, 139 (1998).
25. P. Gopikrishnan, V. Plerou, L. A. N. Amaral, M. Meyer, and H. E. Stanley, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.5305 60, 5305 (1999).
26. R. Rak, S. Drozdz, and J. Kwapien, e-print physics/0603071.
27. Z. Burda, J. Jurkiewicz, M. A. Nowak, G. Papp, and I. Zahed, Physica A PHYADX 0378-4371 343, 694 (2004).
28. Z. Burda, J. Jurkiewicz, and M. A. Nowak, Acta Phys. Pol. B APOBBB 0587-4254 34, 87 (2003).
29. Z. Burda, A. Jarosz, J. Jurkiewicz, M. A. Nowak, G. Papp, and I. Zahed, e-print physics/0603024.
30. G. Le Caër and R. Delannay, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.6281 59, 6281 (1999).
31. R. Delannay and G. Le Caër, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/33/14/302 33, 2611 (2000).
32. F. Toscano, R. O. Vallejos, and C. Tsallis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.066131 69, 066131 (2004).
33. A. C. Bertuola, O. Bohigas, and M. P. Pato, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.065102 70, 065102 (R) (2004).
34. A. Y. Abul-Magd, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.066207 71, 066207 (2005).
35. Z. Burda, A. Görlich, J. Jurkiewicz, and B. Wacław, Eur. Phys. J. B EPJBFY 1434-6028 49, 319 (2006).
36. Z. Burda, J. Jurkiewicz, and B. Wacław, Acta Phys. Pol. B APOBBB 0587-4254 36, 2641 (2005).
37. E. Brezin and A. Zee, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550- 3213(93)90121-5 402, 613 (1993).