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Volumn 41, Issue 3, 2013, Pages 1204-1231

Asymptotic power of sphericity tests for high-dimensional data

Author keywords

Asymptotic power; Contiguity; Contour integral representation; Large dimensionality; Power envelope; Sphericity tests; Spiked covariance; Steepest descent

Indexed keywords


EID: 84879400429     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-AOS1100     Document Type: Article
Times cited : (139)

References (49)
  • 1
    • 0009128834 scopus 로고
    • Convergence rate of expected spectral distributions of large random matrices. II. Sample covariance matrices
    • MR1217560
    • BAI, Z. D. (1993). Convergence rate of expected spectral distributions of large random matrices. II. Sample covariance matrices. Ann. Probab. 21 649-672. MR1217560
    • (1993) Ann. Probab , vol.21 , pp. 649-672
    • Bai, Z.D.1
  • 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
    • 73949135723 scopus 로고    scopus 로고
    • Corrections to LRT on large-dimensional covariance matrix by RMT
    • MR2572444
    • BAI, Z., JIANG, D., YAO, J.-F. and ZHENG, S. (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.1    Jiang, D.2    Yao, J.-F.3    Zheng, S.4
  • 4
    • 27644476898 scopus 로고    scopus 로고
    • Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
    • MR2165575
    • BAIK, J., BEN AROUS, G. and PÉCHÉ, S. (2005). Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 1643-1697. MR2165575
    • (2005) Ann. Probab , vol.33 , pp. 1643-1697
    • Baik, J.1    Ben Arous, G.2    Péché, S.3
  • 5
    • 33646507506 scopus 로고    scopus 로고
    • Eigenvalues of large sample covariance matrices of spiked population models
    • MR2279680
    • BAIK, J. and SILVERSTEIN, J. W. (2006). Eigenvalues of large sample covariance matrices of spiked population models. J. Multivariate Anal. 97 1382-1408. MR2279680
    • (2006) J. Multivariate Anal , vol.97 , pp. 1382-1408
    • Baik, J.1    Silverstein, J.W.2
  • 8
    • 79952832913 scopus 로고    scopus 로고
    • Performance of statistical tests for single source detection using random matrix theory
    • BIANCHI, P., DEBBAH, M.,MAIDA, M. and NAJIM, J. (2011). Performance of statistical tests for single source detection using random matrix theory. IEEE Trans. Inform. Theory 57 2400-2419.
    • (2011) IEEE Trans. Inform. Theory , vol.57 , pp. 2400-2419
    • Bianchi, P.1    Debbah, M.2    Maida, M.3    Najim, J.4
  • 9
    • 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. Statist. Probab. Lett. 74 281-289. MR2189467
    • (2005) Statist. Probab. Lett , vol.74 , pp. 281-289
    • Birke, M.1    Dette, H.2
  • 10
    • 84880640788 scopus 로고    scopus 로고
    • Limits of spiked random matrices i
    • To appear. DOI:10.1007/s00440-012-0443-2. Available at arXiv:1011.1877v2
    • BLOEMENDAL, A. and VIRÁG, B. (2012). Limits of spiked random matrices I. Probab. Theory Related Fields. To appear. DOI:10.1007/s00440-012- 0443-2. Available at arXiv:1011.1877v2.
    • (2012) Probab. Theory Related Fields
    • Bloemendal, A.1    Virág, B.2
  • 11
    • 0036389689 scopus 로고    scopus 로고
    • Laplace approximations for hypergeometric functions with matrix argument
    • MR1926172
    • BUTLER, R.W. andWOOD, A. T. A. (2002). Laplace approximations for hypergeometric functions with matrix argument. Ann. Statist. 30 1155-1177. MR1926172
    • (2002) Ann. Statist , vol.30 , pp. 1155-1177
    • Butler, R.W.1    Wood, A.T.A.2
  • 12
    • 78649411926 scopus 로고    scopus 로고
    • Tests for high-dimensional covariance matrices
    • MR2724863
    • CHEN, S. X., ZHANG, L.-X. and ZHONG, P.-S. (2010). Tests for high-dimensional 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
  • 13
    • 84915676562 scopus 로고
    • Multiple hypergeometric functions: Probabilistic interpretations and statistical uses
    • MR0721212
    • DICKEY, J. M. (1983). Multiple hypergeometric functions: Probabilistic interpretations and statistical uses. J. Amer. Statist. Assoc. 78 628-637. MR0721212
    • (1983) J. Amer. Statist. Assoc , vol.78 , pp. 628-637
    • Dickey, J.M.1
  • 14
    • 46749089905 scopus 로고    scopus 로고
    • Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
    • MR2308592
    • EL KAROUI, N. (2007). Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices. Ann. Probab. 35 663-714. MR2308592
    • (2007) Ann. Probab , vol.35 , pp. 663-714
    • El Karoui, N.1
  • 16
    • 68749084936 scopus 로고    scopus 로고
    • The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case
    • 073302 MR2548630
    • FÉRAL, D. and PÉCHÉ, S. (2009). The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case. J. Math. Phys. 50 073302, 33. MR2548630
    • (2009) J. Math. Phys , vol.50 , pp. 33
    • Féral, D.1    Péché, S.2
  • 17
    • 77956758297 scopus 로고    scopus 로고
    • A new test for sphericity of the covariance matrix for high dimensional data
    • MR2719881
    • FISHER, T. J., SUN, X. and GALLAGHER, C. M. (2010). A new test for sphericity of the covariance matrix for high dimensional data. J. Multivariate Anal. 101 2554-2570. MR2719881
    • (2010) J. Multivariate Anal. , vol.101 , pp. 2554-2570
    • Fisher, T.J.1    Sun, X.2    Gallagher, C.M.3
  • 18
    • 16844362196 scopus 로고    scopus 로고
    • A Fourier view on the R-transform and related asymptotics of spherical integrals
    • MR2132396
    • GUIONNET, A. andMAÏDA, M. (2005). A Fourier view on the R-transform and related asymptotics of spherical integrals. J. Funct. Anal. 222 435-490. MR2132396
    • (2005) J. Funct. Anal. , vol.222 , pp. 435-490
    • Guionnet, A.1    Maïda, M.2
  • 19
    • 34547322109 scopus 로고    scopus 로고
    • Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity
    • MR2329465
    • HALLIN, M. and PAINDAVEINE, D. (2006). Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity. Ann. Statist. 34 2707-2756. MR2329465
    • (2006) Ann. Statist. , Issue.34 , pp. 2707-2756
    • Hallin, M.1    Paindaveine, D.2
  • 20
    • 0035625024 scopus 로고    scopus 로고
    • The density of a quadratic form in a vector uniformly distributed on the nsphere
    • MR1863565
    • HILLIER, G. (2001). The density of a quadratic form in a vector uniformly distributed on the nsphere. Econometric Theory 17 1-28. MR1863565
    • (2001) Econometric Theory , vol.17 , pp. 1-28
    • Hillier, G.1
  • 21
    • 58149310770 scopus 로고    scopus 로고
    • Automatic PCA dimension selection for high dimensional data and small sample sizes
    • HOYLE, D. C. (2008). Automatic PCA dimension selection for high dimensional data and small sample sizes. J. Mach. Learn. Res. 9 2733-2759.
    • (2008) J. Mach. Learn. Res , vol.9 , pp. 2733-2759
    • Hoyle, D.C.1
  • 22
    • 0000952005 scopus 로고
    • Distributions of matrix variates and latent roots derived from normal samples
    • MR0181057
    • JAMES, A. T. (1964). Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35 475-501. MR0181057
    • (1964) Ann. Math. Statist , vol.35 , pp. 475-501
    • James, A.T.1
  • 23
    • 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
  • 24
    • 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
  • 25
    • 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. 29 295-327. MR1863961
    • (2001) Ann. Statist , vol.29 , pp. 295-327
    • Johnstone, I.M.1
  • 26
    • 50249159453 scopus 로고    scopus 로고
    • Determining the number of components in a factor model from limited noisy data
    • KRITCHMAN, S. andNADLER, B. (2008). Determining the number of components in a factor model from limited noisy data. Chemometrics and Intelligent Laboratory Systems 94 19-32.
    • (2008) Chemometrics and Intelligent Laboratory Systems , vol.94 , pp. 19-32
    • Kritchman, S.1    Nadler, B.2
  • 27
    • 70349646485 scopus 로고    scopus 로고
    • Non-parametric detection of the number of signals: Hypothesis testing and random matrix theory
    • MR2683143
    • KRITCHMAN, S. and NADLER, B. (2009). Non-parametric detection of the number of signals: Hypothesis testing and random matrix theory. IEEE Trans. Signal Process. 57 3930-3941. MR2683143
    • (2009) IEEE Trans. Signal Process , vol.57 , pp. 3930-3941
    • Kritchman, S.1    Nadler, B.2
  • 29
    • 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
  • 30
    • 3042549467 scopus 로고    scopus 로고
    • Means of a Dirichlet process and multiple hypergeometric functions
    • MR2060305
    • LIJOI, A. and REGAZZINI, E. (2004). Means of a Dirichlet process and multiple hypergeometric functions. Ann. Probab. 32 1469-1495. MR2060305
    • (2004) Ann. Probab , vol.32 , pp. 1469-1495
    • Lijoi, A.1    Regazzini, E.2
  • 31
    • 0000141380 scopus 로고
    • Significance test for sphericity of a normal n-variate distribution
    • MR0002084
    • MAUCHLY, J. W. (1940). Significance test for sphericity of a normal n-variate distribution. Ann. Math. Statist. 11 204-209. MR0002084
    • (1940) Ann. Math. Statist , vol.11 , pp. 204-209
    • Mauchly, J.W.1
  • 32
    • 84865532215 scopus 로고    scopus 로고
    • Rank 1 real Wishart spiked model
    • MR2969495
    • MO, M. Y. (2012). Rank 1 real Wishart spiked model. Comm. Pure Appl. Math. 65 1528-1638. MR2969495
    • (2012) Comm. Pure Appl. Math. , Issue.65 , pp. 1528-1638
    • Mo, M.Y.1
  • 33
    • 46749116893 scopus 로고    scopus 로고
    • Sample eigenvalue based detection of highdimensional signals in white noise using relatively few samples
    • MR1500236
    • NADAKUDITI, R. R. and EDELMAN, A. (2008). Sample eigenvalue based detection of highdimensional signals in white noise using relatively few samples. IEEE Trans. Signal Process. 56 2625-2638. MR1500236
    • (2008) IEEE Trans. Signal Process , vol.56 , pp. 2625-2638
    • Nadakuditi, R.R.1    Edelman, A.2
  • 34
    • 77952589875 scopus 로고    scopus 로고
    • Fundamental limit of sample generalized eigenvalue based detection of signals in noise using relatively few signal-bearing and noise-only samples
    • NADAKUDITI, R. R. and SILVERSTEIN, J. W. (2010). Fundamental limit of sample generalized eigenvalue based detection of signals in noise using relatively few signal-bearing and noise-only samples. IEEE Journal of Selected Topics in Signal Processing 4 468-480.
    • (2010) IEEE Journal of Selected Topics in Signal Processing , vol.4 , pp. 468-480
    • Nadakuditi, R.R.1    Silverstein, J.W.2
  • 35
    • 62349121558 scopus 로고    scopus 로고
    • Finite sample approximation results for principal component analysis: A matrix perturbation approach
    • MR2485013
    • NADLER, B. (2008). Finite sample approximation results for principal component analysis: A matrix perturbation approach. Ann. Statist. 36 2791-2817. MR2485013
    • (2008) Ann. Statist , vol.36 , pp. 2791-2817
    • Nadler, B.1
  • 37
    • 70349835782 scopus 로고    scopus 로고
    • Testing hypotheses about the numbers of factors in large factor models
    • MR2561070
    • ONATSKI, A. (2009). Testing hypotheses about the numbers of factors in large factor models. Econometrica 77 1447-1479. MR2561070
    • (2009) Econometrica , vol.77 , pp. 1447-1479
    • Onatski, A.1
  • 38
    • 78650967353 scopus 로고    scopus 로고
    • Determining the number of factors from empirical distribution of eigenvalues
    • ONATSKI, A. (2010). Determining the number of factors from empirical distribution of eigenvalues. Rev. Econom. Statist. 92 1004-1016.
    • (2010) Rev. Econom. Statist , vol.92 , pp. 1004-1016
    • Onatski, A.1
  • 40
    • 33846006923 scopus 로고    scopus 로고
    • Population structure and eigenanalysis
    • PATTERSON, N., PRICE, A. L. and REICH, D. (2006). Population structure and eigenanalysis. PLoS Genetics 2 2074-2093.
    • (2006) PLoS Genetics , vol.2 , pp. 2074-2093
    • Patterson, N.1    Price, A.L.2    Reich, D.3
  • 42
    • 27944490752 scopus 로고    scopus 로고
    • A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix
    • MR2256563
    • SCHOTT, J. R. (2006). A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix. J. Multivariate Anal. 97 827-843. MR2256563
    • (2006) J. Multivariate Anal , vol.97 , pp. 827-843
    • Schott, J.R.1
  • 43
    • 0000602132 scopus 로고
    • On the empirical distribution of eigenvalues of a class of large-dimensional random matrices
    • MR1345534
    • SILVERSTEIN, J.W. and BAI, Z. D. (1995). On the empirical distribution of eigenvalues of a class of large-dimensional random matrices. J. Multivariate Anal. 54 175-192. MR1345534
    • (1995) J. Multivariate Anal. , vol.54 , pp. 175-192
    • Silverstein, J.W.1    Bai, Z.D.2
  • 44
    • 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
  • 46
    • 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. Math. Statist. 43 1312-1316. MR0311032
    • (1972) Ann. Math. Statist , vol.43 , pp. 1312-1316
    • Sugiura, N.1
  • 47
    • 21344476194 scopus 로고
    • On singular Wishart and singular multivariate beta distributions
    • MR1272090
    • UHLIG, H. (1994). On singular Wishart and singular multivariate beta distributions. Ann. Statist. 22 395-405. MR1272090
    • (1994) Ann. Statist , vol.22 , pp. 395-405
    • Uhlig, H.1
  • 49
    • 84862812048 scopus 로고    scopus 로고
    • The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, Part I
    • MR2916094
    • WANG, D. (2012). The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, Part I. J. Stat. Phys. 146 719-761. MR2916094
    • (2012) J. Stat. Phys. , vol.146 , pp. 719-761
    • Wang, D.1


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