메뉴 건너뛰기




Volumn 54, Issue 11, 2008, Pages 5113-5129

Improved estimation of eigenvalues and eigenvectors of covariance matrices using their sample estimates

Author keywords

Eigenvalues; Eigenvectors; G estimation; Random matrix theory; Sample covariance matrix

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; RANDOM PROCESSES;

EID: 55349116422     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2008.929938     Document Type: Article
Times cited : (205)

References (31)
  • 1
    • 0000624015 scopus 로고
    • Multiple emitter localization and signal parameter estimation
    • Rome, NY
    • R. Schmidt, "Multiple emitter localization and signal parameter estimation," in Proc. RADC, Spectral Estimation Workshop, Rome, NY, 1979, pp. 243-258.
    • (1979) Proc. RADC, Spectral Estimation Workshop , pp. 243-258
    • Schmidt, R.1
  • 2
    • 0031103096 scopus 로고    scopus 로고
    • A subspace algorithm for certain blind identification problems
    • Mar
    • K. Abed-Meraim, P. Loubaton, and E. Moulines, "A subspace algorithm for certain blind identification problems," IEEE Trans. Inf. Theory, vol. 43, no. 2, pp. 499-511, Mar. 1997.
    • (1997) IEEE Trans. Inf. Theory , vol.43 , Issue.2 , pp. 499-511
    • Abed-Meraim, K.1    Loubaton, P.2    Moulines, E.3
  • 3
    • 0032023746 scopus 로고    scopus 로고
    • Blind multiuser detection: A subspace approach
    • Mar
    • X. Wang and H. V. Poor, "Blind multiuser detection: A subspace approach," IEEE Trans. Inf. Theory, vol. 44, no. 2, pp. 677-690, Mar. 1998.
    • (1998) IEEE Trans. Inf. Theory , vol.44 , Issue.2 , pp. 677-690
    • Wang, X.1    Poor, H.V.2
  • 4
    • 0021892197 scopus 로고
    • Detection of signals by information theoretic criteria
    • Apr
    • M. Wax and T. Kailath, "Detection of signals by information theoretic criteria," IEEE Trans. Acoust., Speech, Signal Process., vol. 33, no. 2, pp. 387-392, Apr. 1985.
    • (1985) IEEE Trans. Acoust., Speech, Signal Process , vol.33 , Issue.2 , pp. 387-392
    • Wax, M.1    Kailath, T.2
  • 5
    • 0001699986 scopus 로고
    • Asymptotic theory for principal component analysis
    • Mar
    • T. Anderson, "Asymptotic theory for principal component analysis," Ann. Math. Statist., vol. 34, pp. 122-148, Mar. 1963.
    • (1963) Ann. Math. Statist , vol.34 , pp. 122-148
    • Anderson, T.1
  • 7
    • 0002844378 scopus 로고
    • Asymptotic theory for principal component analysis in the complex case
    • R. Gupta, "Asymptotic theory for principal component analysis in the complex case," J. Indian Statist. Assoc., vol. 3, pp. 97-106, 1965.
    • (1965) J. Indian Statist. Assoc , vol.3 , pp. 97-106
    • Gupta, R.1
  • 8
    • 0007038401 scopus 로고    scopus 로고
    • Asymptotics of eigenprojections of correlation matrices with some applications in principal component analysis
    • Jun
    • J. Schott, "Asymptotics of eigenprojections of correlation matrices with some applications in principal component analysis," Biometrika vol. 84, pp. 327-337, Jun. 1997.
    • (1997) Biometrika , vol.84 , pp. 327-337
    • Schott, J.1
  • 9
    • 0038532237 scopus 로고
    • An asymptotic expansion for the distribution of the latent roots of the estimated covariance matrix
    • Aug
    • G. Anderson, "An asymptotic expansion for the distribution of the latent roots of the estimated covariance matrix," Ann. Math. Statist., vol. 36, pp. 1153-1173, Aug. 1965.
    • (1965) Ann. Math. Statist , vol.36 , pp. 1153-1173
    • Anderson, G.1
  • 10
    • 0042422712 scopus 로고
    • Developments in Eigenvalue Estimation
    • A. K. Gupta, Ed. Boston, MA: Reidel
    • R. Muirhead, "Developments in Eigenvalue Estimation," in Advances in Multivariate Statistical Analysis, A. K. Gupta, Ed. Boston, MA: Reidel, 1987, pp. 277-288.
    • (1987) Advances in Multivariate Statistical Analysis , pp. 277-288
    • Muirhead, R.1
  • 11
    • 0000406169 scopus 로고
    • Empirical bayes estimation of the multivariate normal covariance matrix
    • May
    • L. Haff, "Empirical bayes estimation of the multivariate normal covariance matrix," Ann. Statist., vol. 8, pp. 586-597, May 1980.
    • (1980) Ann. Statist , vol.8 , pp. 586-597
    • Haff, L.1
  • 12
    • 0000752425 scopus 로고
    • Estimation of a covariance matrix under Stein's loss
    • D. Dey and C. Srinivasan, "Estimation of a covariance matrix under Stein's loss," Ann. Statist., vol. 13, pp. 1581-1591, 1985.
    • (1985) Ann. Statist , vol.13 , pp. 1581-1591
    • Dey, D.1    Srinivasan, C.2
  • 13
    • 0041169168 scopus 로고    scopus 로고
    • Large-sample estimation strategies for eigenvalues of a Wishart matrix
    • S. Ahmed, "Large-sample estimation strategies for eigenvalues of a Wishart matrix," Metrika, vol. 47, pp. 35-45, 1998.
    • (1998) Metrika , vol.47 , pp. 35-45
    • Ahmed, S.1
  • 14
    • 0007229742 scopus 로고
    • Simultaneous estimation of eigenvalues
    • D. Dey, "Simultaneous estimation of eigenvalues," Ann. Inst. Statist. Math., vol. 40, no. 1, pp. 137-147, 1988.
    • (1988) Ann. Inst. Statist. Math , vol.40 , Issue.1 , pp. 137-147
    • Dey, D.1
  • 15
    • 38249005664 scopus 로고
    • A note on simultaneous estimation of eigenvalues of a multivariate normal covariance matrix
    • Feb
    • C. Jin, "A note on simultaneous estimation of eigenvalues of a multivariate normal covariance matrix," Statist. Probab. Lett., vol. 16, pp. 197-203, Feb. 1993.
    • (1993) Statist. Probab. Lett , vol.16 , pp. 197-203
    • Jin, C.1
  • 16
  • 17
    • 0009607169 scopus 로고
    • Asymptotic inference for eigenvectors
    • Jul
    • D. Tyler, "Asymptotic inference for eigenvectors," Ann. Statist. vol. 9, pp. 725-736, Jul. 1981.
    • (1981) Ann. Statist , vol.9 , pp. 725-736
    • Tyler, D.1
  • 18
    • 54949128293 scopus 로고    scopus 로고
    • On the asymptotic behavior of the sample estimates of eigenvalues and eigenvectors of covariance matrices
    • Nov
    • X. Mestre, "On the asymptotic behavior of the sample estimates of eigenvalues and eigenvectors of covariance matrices," IEEE Trans. Signal Process., vol. 56, no. 11, Nov. 2008.
    • (2008) IEEE Trans. Signal Process , vol.56 , Issue.11
    • Mestre, X.1
  • 19
    • 30344466461 scopus 로고
    • G25-estimators of principal components
    • V. Girko, "G25-estimators of principal components," Theory Probab. Math. Statist., vol. 40, pp. 1-10, 1990.
    • (1990) Theory Probab. Math. Statist , vol.40 , pp. 1-10
    • Girko, V.1
  • 20
    • 54949098086 scopus 로고    scopus 로고
    • Strong law for the eigenvalues and eigenvectors of empirical covariance matrices
    • V. Girko, "Strong law for the eigenvalues and eigenvectors of empirical covariance matrices," Random Oper. Stochastic Equations, vol. 4, no. 2, pp. 176-204, 1996.
    • (1996) Random Oper. Stochastic Equations , vol.4 , Issue.2 , pp. 176-204
    • Girko, V.1
  • 21
    • 0002627253 scopus 로고
    • Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices
    • J. Silverstein, "Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices," J. Multivariate Anal., vol. 5, pp. 331-339, 1995.
    • (1995) J. Multivariate Anal , vol.5 , pp. 331-339
    • Silverstein, J.1
  • 22
    • 51549106256 scopus 로고    scopus 로고
    • On asymptotics of eigenvectors of large sample covariance matrix
    • Z. Bai, B. Miao, and G. Pan, "On asymptotics of eigenvectors of large sample covariance matrix," Ann. Probab., vol. 35, no. 4, pp. 1532-1572, 2007.
    • (2007) Ann. Probab , vol.35 , Issue.4 , pp. 1532-1572
    • Bai, Z.1    Miao, B.2    Pan, G.3
  • 23
    • 55349138885 scopus 로고    scopus 로고
    • X. Mestre, On the Asymptotic Behavior of Quadratic Forms of the Resolvent Covariance-Type Matrices, Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain, 2006 [Online]. Available: http://www.cttc.cat/en/person/xmestre/publications.jsp
    • X. Mestre, "On the Asymptotic Behavior of Quadratic Forms of the Resolvent Covariance-Type Matrices," Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain, 2006 [Online]. Available: http://www.cttc.cat/en/person/xmestre/publications.jsp
  • 24
    • 69949168670 scopus 로고    scopus 로고
    • Spectrum Estimation for Large Dimensional Covariance Matrices Using Random Matrix Theory
    • arXiv:mAth/0609418
    • N. E. Karoui, "Spectrum Estimation for Large Dimensional Covariance Matrices Using Random Matrix Theory," arXiv:mAth/0609418.
    • Karoui, N.E.1
  • 25
    • 39649111603 scopus 로고
    • Asymptotic behavior of eigenvalues of empirical covariance matrices
    • V. Girko, "Asymptotic behavior of eigenvalues of empirical covariance matrices," Theory Probab. Math. Statist., vol. 44, pp. 37-44, 1992.
    • (1992) Theory Probab. Math. Statist , vol.44 , pp. 37-44
    • Girko, V.1
  • 26
    • 58149320175 scopus 로고
    • Analysis of the limiting spectral distribution of large dimensional random matrices
    • J. Silverstein and S. Choi, "Analysis of the limiting spectral distribution of large dimensional random matrices," J. Multivariate Anal., vol. 54, pp. 295-309, 1995.
    • (1995) J. Multivariate Anal , vol.54 , pp. 295-309
    • Silverstein, J.1    Choi, S.2
  • 27
    • 22044453079 scopus 로고    scopus 로고
    • No eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices
    • Z. Bai and J. Silverstein, "No eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices," Ann. Probab., vol. 26, pp. 316-345, 1998.
    • (1998) Ann. Probab , vol.26 , pp. 316-345
    • Bai, Z.1    Silverstein, J.2
  • 28
    • 0042112495 scopus 로고
    • A limit theorem for the eigenvalues of product of two random matrices
    • Dec
    • Y. Yin and P. Krishnaiah, "A limit theorem for the eigenvalues of product of two random matrices," J. Multivariate Anal., vol. 13, pp. 489-507, Dec. 1983.
    • (1983) J. Multivariate Anal , vol.13 , pp. 489-507
    • Yin, Y.1    Krishnaiah, P.2
  • 29
    • 0347989448 scopus 로고    scopus 로고
    • Methodologies in spectral analysis of large dimensional random matrices, a review
    • Z. Bai, "Methodologies in spectral analysis of large dimensional random matrices, a review," Statist. Sinica, vol. 9, pp. 611-677, 1999.
    • (1999) Statist. Sinica , vol.9 , pp. 611-677
    • Bai, Z.1
  • 30
    • 0033164056 scopus 로고    scopus 로고
    • Exact separation of eigenvalues of large dimensional sample covariance matrices
    • Z. Bai and J. Silverstein, "Exact separation of eigenvalues of large dimensional sample covariance matrices," Ann. Probab., vol. 27, no. 3, pp. 1536-1555, 1999.
    • (1999) Ann. Probab , vol.27 , Issue.3 , pp. 1536-1555
    • Bai, Z.1    Silverstein, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.