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Olivier Ledoit, Michael Wolf (2002)
Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample sizeQuality Engineering, 48
T. Anderson (1985)
An Introduction to Multivariate Statistical Analysis, 2nd Edition.Biometrics, 41
I. Johnstone (2001)
On the distribution of the largest eigenvalue in principal components analysisAnnals of Statistics, 29
X. Tian, Yuting Lu, Weiming Li (2015)
A robust test for sphericity of high-dimensional covariance matricesJ. Multivar. Anal., 141
H. Nagao (1973)
On Some Test Criteria for Covariance MatrixAnnals of Statistics, 1
Z. Bai, J. Silverstein (2009)
Spectral Analysis of Large Dimensional Random Matrices
M. Srivastava (2005)
Some Tests Concerning the Covariance Matrix in High Dimensional DataJournal of the Japan Statistical Society. Japanese issue, 35
Hao Wang, Baisen Liu, N. Shi, Shu-rong Zheng (2018)
Testing identity of high-dimensional covariance matrixJournal of Statistical Computation and Simulation, 88
M. Torun, A. Akansu, M. Avellaneda (2011)
Portfolio Risk in Multiple FrequenciesIEEE Signal Processing Magazine, 28
Thomas Fisher (2012)
On testing for an identity covariance matrix when the dimensionality equals or exceeds the sample sizeJournal of Statistical Planning and Inference, 142
R. Nadakuditi, A. Edelman (2007)
Sample Eigenvalue Based Detection of High-Dimensional Signals in White Noise Using Relatively Few SamplesIEEE Transactions on Signal Processing, 56
Shu-rong Zheng (2012)
Central limit theorems for linear spectral statistics of large dimensional F-matricesAnnales De L Institut Henri Poincare-probabilites Et Statistiques, 48
Qinwen Wang, Jianfeng Yao (2013)
On the sphericity test with large-dimensional observationsarXiv: Statistics Theory
J. Silverstein (1995)
Strong convergence of the empirical distribution of eigenvalues of large dimensional random matricesJournal of Multivariate Analysis, 55
P. Bianchi, M. Debbah, Mylène Maïda, J. Najim (2009)
Performance of Statistical Tests for Single-Source Detection Using Random Matrix TheoryIEEE Transactions on Information Theory, 57
M. Srivastava (2006)
Some tests criteria for the covariance matrix with fewer observations than the dimensionActa et Commentationes Universitatis Tartuensis de Mathematica
Zhidong Bai, J. Silverstein (2008)
CLT for linear spectral statistics of large-dimensional sample covariance matricesAnnals of Probability, 32
S. John (1971)
Some optimal multivariate testsBiometrika, 58
Cheng Wang, J. Yang, B. Miao, Longbing Cao (2012)
Identity tests for high dimensional data using RMTJ. Multivar. Anal., 118
M. Srivastava, H. Yanagihara (2010)
Testing the equality of several covariance matrices with fewer observations than the dimensionJ. Multivar. Anal., 101
Romain Couillet, W. Hachem (2011)
Fluctuations of Spiked Random Matrix Models and Failure Diagnosis in Sensor NetworksIEEE Transactions on Information Theory, 59
Songxi Chen, Lixu Zhang, Pingshou Zhong (2010)
Tests for High-Dimensional Covariance MatricesJournal of the American Statistical Association, 105
M. Dettling (2004)
BagBoosting for tumor classification with gene expression dataBioinformatics, 20 18
Thomas Fisher, Xiaoqian Sun, C. Gallagher (2010)
A new test for sphericity of the covariance matrix for high dimensional dataJ. Multivar. Anal., 101
M. Birke, H. Dette (2005)
A note on testing the covariance matrix for large dimensionStatistics & Probability Letters, 74
Romain Couillet, M. Debbah (2011)
Random Matrix Methods for Wireless Communications: Applications to wireless communications
G. Pan, Wang Zhou (2008)
Central limit theorem for signal-to-interference ratio of reduced rank linear receiverAnnals of Applied Probability, 18
Todd Golub, Todd Golub, D. Slonim, Pablo Tamayo, Christine Huard, Michelle Gaasenbeek, J. Mesirov, Hilary Coller, M. Loh, James Downing, Michael Caligiuri, C. Bloomfield, Eric Lander (1999)
Molecular classification of cancer: class discovery and class prediction by gene expression monitoring.Science, 286 5439
Z. Bai, Dandan Jiang, J. Yao, Shu-rong Zheng (2009)
Corrections to LRT on large-dimensional covariance matrix by RMTAnnals of Statistics, 37
S. Dudoit, J. Fridlyand, T. Speed (2002)
Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression DataJournal of the American Statistical Association, 97
M. Srivastava, T. Kollo, D. Rosen (2011)
Some tests for the covariance matrix with fewer observations than the dimension under non-normalityJ. Multivar. Anal., 102
M. Dettling, P. Bühlmann (2003)
Boosting for Tumor Classification with Gene Expression DataBioinformatics, 19 9
Jiang Hu, Weiming Li, Zhi Liu, Wang Zhou (2018)
High-dimensional covariance matrices in elliptical distributions with application to spherical testThe Annals of Statistics
This paper addresses the issue of testing sphericity and identity of high-dimensional population covariance matrix when the data dimension exceeds the sample size. The central limit theorem of the first four moments of eigenvalues of sample covariance matrix is derived using random matrix theory for generally distributed populations. Further, some desirable asymptotic properties of the proposed test statistics are provided under the null hypothesis as data dimension and sample size both tend to infinity. Simulations show that the proposed tests have a greater power than existing methods for the spiked covariance model.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Apr 24, 2021
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