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In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions.
Test of significance in factor analysis
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Determining the number of factors in approximate factor models
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Inference theory for factor models of large dimensions
J. Bai · 2003
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CLT for linear spectral statistics of large-dimensional sample covariance matrices
Z. Bai and J. W. Silverstein · 2004
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High dimensional statistical inference and random matrices
I. M. Johnstone · 2007
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Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
D. Paul · 2007
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Central limit theorems for eigenvalues in a spiked population model
Z. Bai and J. Yao · 2008
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Dimension estimation in noisy PCA with SURE and random matrix theory
M. O. Ulfarsson and V. Solo · 2008
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Spectral analysis of large dimensional random matrices
Z. Bai and J. W. Silverstein · 2010
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On estimation of the population spectral distribution from a high-dimensional sample covariance matrix
Z. Bai, J. Chen, and J. Yao · 2010
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Bayesian robust principal component analysis
X. Ding, L. He, and L. Carin · 2011
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Statistical analysis of factor models of high dimension
J. Bai and K. Li · 2012
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A quasi–maximum likelihood approach for large, approximate dynamic factor models
C. Doz, D. Giannone, and L. Reichlin · 2012
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On determining the number of spikes in a high-dimensional spiked population model
D. Passemier and J. Yao · 2012
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Corrections to LRT on large-dimensional covariance matrix by RMT
Z. Bai, D. Jiang, J. Yao, and S. Zheng · 2009
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On consistency and sparsity for principal components analysis in high dimensions
I. M Johnstone and A. Y. Lu · 2009
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Statistical challenges of high-dimensional data
I. M. Johnstone and D. M. Titterington · 2009
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Testing hypotheses about the number of factors in large factor models
A. Onatski · 2009
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Estimation of spiked eigenvalues in spiked models
Z. Bai and X. Ding · 2010
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Eigenvalues of large sample covariance matrices of spiked population models
J. Baik and J. W. Silverstein
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Central limit theorems for linear spectral statistics of large dimensional f-matrices
S. Zheng · 2012
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Sparse principal component analysis and iterative thresholding
Z. Ma · 2013
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A note on the CLT of the LSS for sample covariance matrix from a spiked population model
Q. Wang, J. W. Silverstein, and J. Yao · 2013
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S. Zheng, Z. Bai, and J. Yao · 2014
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