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Volumn 7, Issue 1, 2013, Pages 2164-2192

On the sphericity test with large-dimensional observations

Author keywords

CLT for linear spectral statistics; John's test; Large dimensional data; Large dimensional sample covariance matrix; Likelihood ratio test; Nagao's test; Sphericity; Spiked population model

Indexed keywords


EID: 84884942640     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-EJS842     Document Type: Article
Times cited : (75)

References (30)
  • 2
    • 2142823889 scopus 로고    scopus 로고
    • CLT for linear spectral statistics of large-dimensional sample covariance matrices
    • MR2040792
    • Bai, Z.D. and Silverstein, J.W. (2004). CLT for linear spectral statistics of large-dimensional sample covariance matrices. Ann. Probab., 32, 553-605. MR2040792
    • (2004) Ann. Probab. , vol.32 , pp. 553-605
    • Bai, Z.D.1    Silverstein, J.W.2
  • 3
    • 33645671934 scopus 로고    scopus 로고
    • On the convergence of the spectral empirical process of Wigner matrices
    • MR2189081
    • Bai, Z.D. and Yao, J.F. (2005). On the convergence of the spectral empirical process of Wigner matrices. Bernoulli, 11(6), 1059-1092. MR2189081
    • (2005) Bernoulli , vol.11 , Issue.6 , pp. 1059-1092
    • Bai, Z.D.1    Yao, J.F.2
  • 4
    • 73949135723 scopus 로고    scopus 로고
    • Corrections to LRT on large-dimensional covariance matrix by RMT
    • MR2572444
    • Bai, Z.D., Jiang, D.D., Yao, J.F., and Zheng, S.R. (2009). Corrections to LRT on large-dimensional covariance matrix by RMT. Ann. Statist., 37, 3822-3840. MR2572444
    • (2009) Ann. Statist. , vol.37 , pp. 3822-3840
    • Bai, Z.D.1    Jiang, D.D.2    Yao, J.F.3    Zheng, S.R.4
  • 6
    • 84884943863 scopus 로고    scopus 로고
    • Testing linear hypotheses in high-dimensional regressions
    • doi:10.1080/02331888.2012.708031
    • Bai, Z.D., Jiang, D.D., Yao, J.F., and Zheng, S.R. (2012). Testing linear hypotheses in high-dimensional regressions. Statistics, doi:10.1080/02331888.2012.708031.
    • (2012) Statistics
    • Bai, Z.D.1    Jiang, D.D.2    Yao, J.F.3    Zheng, S.R.4
  • 7
    • 23944490887 scopus 로고    scopus 로고
    • A note on testing the covariance matrix for large dimension
    • MR2189467
    • Birke, M. and Dette, H. (2005). A note on testing the covariance matrix for large dimension. Statistics and Probability Letters, 74, 281-289. MR2189467
    • (2005) Statistics and Probability Letters , vol.74 , pp. 281-289
    • Birke, M.1    Dette, H.2
  • 8
    • 77649330805 scopus 로고    scopus 로고
    • A two-sample test for high-dimensional data with applications to gene-set testing
    • MR2604697
    • Chen, S.X. and Qin, Y.L. (2010). A two-sample test for high-dimensional data with applications to gene-set testing. Ann. Statist., 38, 808-835. MR2604697
    • (2010) Ann. Statist. , vol.38 , pp. 808-835
    • Chen, S.X.1    Qin, Y.L.2
  • 9
    • 78649411926 scopus 로고    scopus 로고
    • Tests for highdimensional covariance matrices
    • MR2724863
    • Chen, S.X., Zhang, L.X., and Zhong, P.S. (2010). Tests for highdimensional covariance matrices. J. Amer. Statist. Assoc., 105, 810-819. MR2724863
    • (2010) J. Amer. Statist. Assoc. , vol.105 , pp. 810-819
    • Chen, S.X.1    Zhang, L.X.2    Zhong, P.S.3
  • 10
    • 0041611613 scopus 로고
    • Some optimal multivariate tests
    • MR0275568
    • John, S. (1971). Some optimal multivariate tests. Biometrika, 58, 123-127. MR0275568
    • (1971) Biometrika , vol.58 , pp. 123-127
    • John, S.1
  • 11
    • 0042613506 scopus 로고
    • The distribution of a statistic used for testing sphericity of normal distributions
    • MR0312619
    • John, S. (1972). The distribution of a statistic used for testing sphericity of normal distributions. Biometrika, 59, 169-173. MR0312619
    • (1972) Biometrika , vol.59 , pp. 169-173
    • John, S.1
  • 12
    • 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), 1-38. MR0650926
    • (1982) J. Multivariate Anal. , vol.12 , Issue.1 , pp. 1-38
    • Jonsson, D.1
  • 13
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • MR1863961
    • Johnstone, I.M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist., 29(2), 295-327. MR1863961
    • (2001) Ann. Statist. , vol.29 , Issue.2 , pp. 295-327
    • Johnstone, I.M.1
  • 15
    • 0036392431 scopus 로고    scopus 로고
    • Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size
    • MR1926169
    • Ledoit, O. and Wolf, M. (2002). Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. Ann. Statist., 30, 1081-1102. MR1926169
    • (2002) Ann. Statist. , vol.30 , pp. 1081-1102
    • Ledoit, O.1    Wolf, M.2
  • 16
    • 59549093885 scopus 로고    scopus 로고
    • Central limit theorem for linear eigenvalue statistics of the Wigner and the sample covariance random matrices
    • MR2481919
    • Lytova, A. and Pastur, L. (2009). Central limit theorem for linear eigenvalue statistics of the Wigner and the sample covariance random matrices. Metrika, 69, 153-172. MR2481919
    • (2009) Metrika , vol.69 , pp. 153-172
    • Lytova, A.1    Pastur, L.2
  • 17
    • 0000141380 scopus 로고
    • Test for sphericity of a normal n-variate distribution
    • MR0002084
    • Mauchly, J.W. (1940). Test for sphericity of a normal n-variate distribution. Ann. Mathe. Statist., 11, 204-209. MR0002084
    • (1940) Ann. Mathe. Statist. , vol.11 , pp. 204-209
    • Mauchly, J.W.1
  • 19
    • 0000029216 scopus 로고
    • On some test criteria for covariance matrix
    • MR0339405
    • Nagao, H. (1973). On some test criteria for covariance matrix. Ann. Statist., 1, 700-709. MR0339405
    • (1973) Ann. Statist. , vol.1 , pp. 700-709
    • Nagao, H.1
  • 20
    • 84879400429 scopus 로고    scopus 로고
    • Asymptotic power of sphericity tests for high-dimensional data
    • Onatski, A., Moreira, M.J., and Hallin, M. (2013). Asymptotic power of sphericity tests for high-dimensional data. Ann. Statist., 41(3), 1204-1231.
    • (2013) Ann. Statist. , vol.41 , Issue.3 , pp. 1204-1231
    • Onatski, A.1    Moreira, M.J.2    Hallin, M.3
  • 21
    • 52949113042 scopus 로고    scopus 로고
    • Central limit theorem for signal-tointerference ratio of reduced rank linear receiver
    • MR2418244
    • Pan, G.M. and Zhou, W. (2008). Central limit theorem for signal-tointerference ratio of reduced rank linear receiver. Ann. Appl. Probab., 18, 1232-1270. MR2418244
    • (2008) Ann. Appl. Probab. , vol.18 , pp. 1232-1270
    • Pan, G.M.1    Zhou, W.2
  • 22
    • 84884928762 scopus 로고    scopus 로고
    • Comparision between two types of large sample covariance matrices
    • To appear in
    • Pan, G.M. (2012). Comparision between two types of large sample covariance matrices. To appear in Ann. Institut Henri Poincaré.
    • (2012) Ann. Institut Henri Poincaré
    • Pan, G.M.1
  • 23
    • 34548834688 scopus 로고    scopus 로고
    • Some high-dimensional tests for a one-way MANOVA
    • MR2392435
    • Schott, J.R. (2007). Some high-dimensional tests for a one-way MANOVA. J. Multivariate Anal., 98, 1825-1839. MR2392435
    • (2007) J. Multivariate Anal. , vol.98 , pp. 1825-1839
    • Schott, J.R.1
  • 24
    • 33748417779 scopus 로고    scopus 로고
    • Some tests concerning the covariance matrix in high dimensional data
    • MR2328427
    • Srivastava, M.S. (2005). Some tests concerning the covariance matrix in high dimensional data. J. Japan Statist. Soc., 35, 251-272. MR2328427
    • (2005) J. Japan Statist. Soc. , vol.35 , pp. 251-272
    • Srivastava, M.S.1
  • 25
    • 33748413613 scopus 로고    scopus 로고
    • Multivariate analysis of variance with fewer observations than the dimension
    • MR2301265
    • Srivastava, M.S. and Fujikoshi, Y. (2006). Multivariate analysis of variance with fewer observations than the dimension. J. Multiv. Anal., 97, 1927-1940. MR2301265
    • (2006) J. Multiv. Anal. , vol.97 , pp. 1927-1940
    • Srivastava, M.S.1    Fujikoshi, Y.2
  • 26
    • 79954642379 scopus 로고    scopus 로고
    • Some tests for the covariance matrix with fewer observations than the dimension under non-normality
    • MR2793878
    • Srivastava, M.S., Kollo, T., and Rosen, D. (2011). Some tests for the covariance matrix with fewer observations than the dimension under non-normality. J. Multiv. Anal., 102, 1090-1103. MR2793878
    • (2011) J. Multiv. Anal. , vol.102 , pp. 1090-1103
    • Srivastava, M.S.1    Kollo, T.2    Rosen, D.3
  • 27
    • 30244441868 scopus 로고
    • Locally best invariant test for sphericity and the limiting distributions
    • MR0311032
    • Sugiura, N. (1972). Locally best invariant test for sphericity and the limiting distributions. Ann. Mathe. Statist., 43, 1312-1316. MR0311032
    • (1972) Ann. Mathe. Statist. , vol.43 , pp. 1312-1316
    • Sugiura, N.1
  • 29
    • 84871929900 scopus 로고    scopus 로고
    • Central limit theorem for linear spectral statistics of large dimensional F matrix
    • MR2954263
    • Zheng, S.R. (2012). Central limit theorem for linear spectral statistics of large dimensional F matrix. Ann. Institut Henri Poincaré Probab. Statist., 48, 444-476. MR2954263
    • (2012) Ann. Institut Henri Poincaré Probab. Statist. , vol.48 , pp. 444-476
    • Zheng, S.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.