메뉴 건너뛰기




Volumn 16, Issue 4, 2010, Pages 1086-1113

Functional CLT for sample covariance matrices

Author keywords

Bernstein polynomial; Central limit theorem; Sample covariance matrices; Stieltjes transform

Indexed keywords


EID: 79251575877     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/10-BEJ250     Document Type: Article
Times cited : (25)

References (19)
  • 2
    • 0009128834 scopus 로고
    • Convergence rate of expected spectral distributions of large random matrices. Part II. Sample covariance matrices
    • Bai, Z.D. (1993). Convergence rate of expected spectral distributions of large random matrices. Part II. Sample covariance matrices. Ann. Probab. 21 649-672.
    • (1993) Ann. Probab. , vol.21 , pp. 649-672
    • Bai, Z.D.1
  • 3
    • 0347989448 scopus 로고    scopus 로고
    • Methodologies in spectral analysis of large dimensional random matrices, a review
    • Bai, Z.D. (1999). Methodologies in spectral analysis of large dimensional random matrices, a review. Statist. Sinica 9 611-677.
    • (1999) Statist. Sinica , vol.9 , pp. 611-677
    • Bai, Z.D.1
  • 4
    • 84983319269 scopus 로고    scopus 로고
    • A note on the convergence rate of the spectral distributions of large random matrices
    • Bai, Z.D., Miao, B.Q. and Tsay, J. (1997). A note on the convergence rate of the spectral distributions of large random matrices. Statist. Probab. Lett. 34 95-102.
    • (1997) Statist. Probab. Lett. , vol.34 , pp. 95-102
    • Bai, Z.D.1    Miao, B.Q.2    Tsay, J.3
  • 5
    • 1342310020 scopus 로고    scopus 로고
    • Convergence rates of spectral distributions of large sample covariance matrices
    • Bai, Z.D., Miao, B.Q. and Yao, J.F. (2003). Convergence rates of spectral distributions of large sample covariance matrices. SIAM J. Matrix Anal. Appl. 25 105-127.
    • (2003) SIAM J. Matrix Anal. Appl. , vol.25 , pp. 105-127
    • Bai, Z.D.1    Miao, B.Q.2    Yao, J.F.3
  • 6
    • 22044453079 scopus 로고    scopus 로고
    • No eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices
    • Bai, Z.D. and Silverstein, J.W. (1998). No eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices. Ann. Probab. 26 316-345.
    • (1998) Ann. Probab. , vol.26 , pp. 316-345
    • Bai, Z.D.1    Silverstein, J.W.2
  • 7
    • 2142823889 scopus 로고    scopus 로고
    • CLT for linear spectral statistics of large-dimensional sample covariance matrices
    • Bai, Z.D. and Silverstein, J.W. (2004). CLT for linear spectral statistics of large-dimensional sample covariance matrices. Ann. Probab. 32 553-605.
    • (2004) Ann. Probab. , vol.32 , pp. 553-605
    • Bai, Z.D.1    Silverstein, J.W.2
  • 8
    • 44249126145 scopus 로고    scopus 로고
    • Spectral analysis of large dimensional random matrices
    • Beijing: Science Press
    • Bai, Z.D. and Silverstein, J.W. (2006). Spectral Analysis of Large Dimensional Random Matrices. Mathematics Monograph Series 2. Beijing: Science Press.
    • (2006) Mathematics Monograph Series , vol.2
    • Bai, Z.D.1    Silverstein, J.W.2
  • 10
    • 0002455942 scopus 로고
    • Distribution function inequalities for martingales
    • Burkholder, D.L. (1973). Distribution function inequalities for martingales. Ann. Probab. 1 19-42.
    • (1973) Ann. Probab. , vol.1 , pp. 19-42
    • Burkholder, D.L.1
  • 11
    • 0001398639 scopus 로고
    • Spectral analysis of networks with random topologies
    • Grenander, U. and Silverstein, J.W. (1977). Spectral analysis of networks with random topologies. SIAM J. Appl. Math. 32 499-519.
    • (1977) SIAM J. Appl. Math. , vol.32 , pp. 499-519
    • Grenander, U.1    Silverstein, J.W.2
  • 12
    • 0001967458 scopus 로고
    • Some limit theorems for the eigenvalues of a sample covariance matrix
    • Jonsson, D. (1982). Some limit theorems for the eigenvalues of a sample covariance matrix. J. Multivariate Anal. 12 1-38.
    • (1982) J. Multivariate Anal. , vol.12 , pp. 1-38
    • Jonsson, D.1
  • 13
    • 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
  • 14
    • 77149139140 scopus 로고    scopus 로고
    • Central Limit Theorem for linear eigenvalue statistics of random matrices with independent entries
    • Pastur, L.A. and Lytova, A. (2008). Central Limit Theorem for linear eigenvalue statistics of random matrices with independent entries. Ann. Probab. 37 1778-1840.
    • (2008) Ann. Probab. , vol.37 , pp. 1778-1840
    • Pastur, L.A.1    Lytova, A.2
  • 16
    • 0002627253 scopus 로고
    • Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices
    • Silverstein, J.W. (1995). Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices. J. Multivariate Anal. 55 331-339.
    • (1995) J. Multivariate Anal. , vol.55 , pp. 331-339
    • Silverstein, J.W.1
  • 17
    • 0002247902 scopus 로고
    • The strong limits of random matrix spectra for sample matrices of independent elements
    • Wachter, K.W. (1978). The strong limits of random matrix spectra for sample matrices of independent elements. Ann. Statist. 6 1-18.
    • (1978) Ann. Statist. , vol.6 , pp. 1-18
    • Wachter, K.W.1
  • 18
    • 0003059603 scopus 로고
    • Limiting spectral distribution for a class of random matrices
    • Yin, Y.Q. (1986). Limiting spectral distribution for a class of random matrices. J. Multivariate Anal. 20 50-68.
    • (1986) J. Multivariate Anal. , vol.20 , pp. 50-68
    • Yin, Y.Q.1
  • 19
    • 0001136512 scopus 로고
    • On limit of the largest eignevalue of the large dimensional sample covariance matrix
    • Yin, Y.Q., Bai, Z.D. and Krishnaiah, P.R. (1988). On limit of the largest eignevalue of the large dimensional sample covariance matrix. Probab. Theory Related Fields 78 509-521.
    • (1988) Probab. Theory Related Fields , vol.78 , pp. 509-521
    • Yin, Y.Q.1    Bai, Z.D.2    Krishnaiah, P.R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.