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Volumn 18, Issue 4, 2012, Pages 1405-1420

Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero

Author keywords

Empirical distribution; Maximum eigenvalue; Random matrices

Indexed keywords


EID: 84873377152     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/11-BEJ381     Document Type: Article
Times cited : (31)

References (11)
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  • 2
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  • 3
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    • Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix
    • MR1235416
    • Bai, Z.D. and Yin, Y.Q. (1993). Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix. Ann. Probab. 21 1275-1294. MR1235416
    • (1993) Ann. Probab. , vol.21 , pp. 1275-1294
    • Bai, Z.D.1    Yin, Y.Q.2
  • 4
    • 62349123505 scopus 로고    scopus 로고
    • Operator norm consistent estimation of large-dimensional sparse covariance matrices
    • MR2485011
    • El Karoui, N. (2008). Operator norm consistent estimation of large-dimensional sparse covariance matrices. Ann. Statist. 36 2717-2756. MR2485011
    • (2008) Ann. Statist. , vol.36 , pp. 2717-2756
    • El Karoui, N.1
  • 6
    • 0000282987 scopus 로고
    • Maximum properties and inequalities for the eigenvalues of completely continuous operators
    • MR0045952
    • Fan, K. (1951). Maximum properties and inequalities for the eigenvalues of completely continuous operators. Proc. Natl. Acad. Sci. USA 37 760-766. MR0045952
    • (1951) Proc. Natl. Acad. Sci. USA , vol.37 , pp. 760-766
    • Fan, K.1
  • 7
    • 0001436319 scopus 로고
    • A limit theorem for the norm of random matrices
    • MR0566592
    • Geman, S. (1980). A limit theorem for the norm of random matrices. Ann. Probab. 8 252-261. MR0566592
    • (1980) Ann. Probab. , vol.8 , pp. 252-261
    • Geman, S.1
  • 8
    • 0001967458 scopus 로고
    • Some limit theorems for the eigenvalues of a sample covariance matrix
    • MR0650926
    • Jonsson, D. (1982). Some limit theorems for the eigenvalues of a sample covariance matrix. J. Multivariate Anal. 12 1-38. MR0650926
    • (1982) J. Multivariate Anal. , vol.12 , pp. 1-38
    • Jonsson, D.1
  • 9
    • 0000263234 scopus 로고
    • Distribution for some sets of random matrices
    • Marčenko, V.A. and Pastur, L.A. (1967). Distribution for some sets of random matrices. Math. USSRSb. 1 457-483.
    • (1967) Math. USSRSb. , vol.1 , pp. 457-483
    • Marčenko, V.A.1    Pastur, L.A.2
  • 10
    • 0001560594 scopus 로고
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    • Wigner, E.P. (1958). On the distribution of the roots of certain symmetric matrices. Ann. of Math. (2) 67 325-327. MR0095527
    • (1958) Ann. of Math. 2 , vol.67 , pp. 325-327
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  • 11
    • 0001136512 scopus 로고
    • On the limit of the largest eigenvalue of the largedimensional sample covariance matrix
    • MR0950344
    • Yin, Y.Q., Bai, Z.D. and Krishnaiah, P.R. (1988). On the limit of the largest eigenvalue of the largedimensional sample covariance matrix. Probab. Theory Related Fields 78 509-521. MR0950344
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    • Yin, Y.Q.1    Bai, Z.D.2    Krishnaiah, P.R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.