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The aim of this paper is to establish several deep theoretical properties of principal component analysis for multiple-component spike covariance models.
[author] Anderson, T.W.T. (1963). Asymptotic theory for principal component analysis. The Annals of Mathematical Statistics 34 122–148
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[author] Baik, J.J., Ben Arous, G.G. and Péché, S.S. (2005). Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. The Annals of Probability 33 1643–1697
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[author] Hall, P.P., Marron, J.S.J. and Neeman, A.A. (2005). Geometric representation of high dimension, low sample size data. Journal of the Royal Statistical Society: Series B 67 427–444
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[author] Baik, J.J. and Silverstein, J.W.J. (2006). Eigenvalues of large sample covariance matrices of spiked population models. Journal of Multivariate Analysis 97 1382–1408
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[author] Onatski, A.A. (2006). Asymptotic distribution of the principal components estimator of large factor models when factors are relatively weak. Manuscript, Columbia University
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[author] Paul, D.D. (2007). Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statistica Sinica 17 1617–1642
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[author] Paul, D.D. and Johnstone, I.I. (2007). Augmented sparse principal component analysis for high-dimensional data. Technical Report, UC Davis
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[author] Nadler, B.B. (2008). Finite sample approximation results for principal component analysis: A matrix perturbation approach. The Annals of Statistics 36 2791–2817
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[author] Johnstone, I.M.I. and Lu, A.Y.A. (2009). On consistency and sparsity for principal components analysis in high dimensions. Journal of the American Statistical Association 104 682–693
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[author] Jung, S.S. and Marron, J.S.J. (2009). PCA consistency in high dimension, low sample size context. The Annals of Statistics 37 4104–4130
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[author] Cabanski, C.R.C., Qi, Y.Y., Yin, X.X., Bair, E.E., Hayward, M.C.M., Fan, C.C., Li, J.J., Wilkerson, M.D.M., Marron, JSJ., Perou, C.M.C. and Hayes, D.N.D. (2010). SWISS MADE: standardized within class sum of squares to evaluate methodologies and dataset elements. PloS One 5 e9905
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2012
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[author] Yata, K.K. and Aoshima, M.M. (2012). Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations. Journal of Multivariate Analysis 105 193–215
2012
Later among the works it cites.
2012
Later among the works it cites.
[author] Cai, TonyT., Fan, JianqingJ. and Jiang, TiefengT. (2013). Distributions of angles in random packing on spheres. Technical Report
2013
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[author] Lee, S.S., Zou, F.F. and Wright, F. A.F. A. (2010). Convergence and prediction of principal component scores in high-dimensional settings. The Annals of Statistics 38 3605–3629
2010
Cited alongside, same era.
[author] Benaych-Georges, F.F. and Nadakuditi, R.R.R. (2011). The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Advances in Mathematics 227 494–521
2011
Cited alongside, same era.
[author] Jung, S.S., Sen, A.A. and Marron, JSJ. (2012). Boundary behavior in high dimension, low sample size asymptotics of PCA. Journal of Multivariate Analysis 109 190–203
2012
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[author] Fan, JianqingJ., Liao, YuanY. and Mincheva, MartinaM. (2013). Large covariance estimation by thresholding principal orthogonal complements. Journal of the Royal Statistical Society: Series B 75 1–44
2013
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[author] Shen, D.D., Shen, H.H., Zhu, H.H. and Marron, J.S.J. (2013). Surprising asymptotic conical structure in critical sample eigen-directions: supplementary materials. Available online at http://www.unc.edu/ dshen/BBPCA/BBPCASupplement.pdf
2013
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