Fetching the paper…
Reading the bibliography…
In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible.
Distribution of eigenvalues for some sets of random matrices
V.A. Marčenko, L.A. Pastur · 1967
Earlier work this paper cites.
The Annals of Statistics
D.E.Tyler. Asymptotic inference for eigenvectors · 1981
Earlier work this paper cites.
The Annals of Statistics
D.E.Tyler. A class of asymptotic tests for principal component vectors · 1983
Earlier work this paper cites.
Approximating Confidence Intervals for Factor Loadings
Z.V. Lambert, A.R. Wildt, and R. M. Durand · 1991
Earlier work this paper cites.
Asymptotic properties of large random matrices with independent entries
A.M. Khorunzhy, B.A. Khoruzhenko, and L.A. Pastur · 1996
Earlier work this paper cites.
On the distribution of the largest eigenvalue in principal components analysis
I. Johnstone · 2001
Earlier work this paper cites.
Determining the Number of Factors in Approximate Factor Models
J. Bai, and S. Ng · 2002
Earlier work this paper cites.
Principal Component Analysis
I. T. Jolliffe · 2002
Earlier work this paper cites.
An Introduction to Multivariate Statistical Analysis, 3rd edition
T. Anderson · 2003
Earlier work this paper cites.
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
J. Baik, G. Ben Arous, and S. Péché · 2005
Earlier work this paper cites.
Eigenvalues of large sample covariance matrices of spiked population models
J. Baik, J.W. Silverstein · 2006
Earlier work this paper cites.
The largest eigenvalue of small rank perturbations of Hermitian random matrices
S. Péché · 2006
Earlier work this paper cites.
Sparse Principal Component Analysis
H. Zou, T. Hastie, and R. Tibshirani · 2006
Earlier work this paper cites.
The largest eigenvalue of rank one deformation of large Wigner matrices
D. Féral, S. Péché · 2007
Earlier work this paper cites.
Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
D. Paul · 2007
Earlier work this paper cites.
Central limit theorems for eigenvalues in a spiked population model
Z.D. Bai, J.F. Yao · 2008
Earlier work this paper cites.
Sample eigenvalue based detection of high-dimensional signals in white noise using relatively few samples
R. R. Nadakuditi, and A., Edelman · 2008
Earlier work this paper cites.
Finite sample approximation results for principal component analysis: A matrix perturbation approach
B. Nadler · 2008
Earlier work this paper cites.
Sparse principal component analysis via regularized low rank matrix approximation
H. Shen, and J. Huang · 2008
Earlier work this paper cites.
The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations
M. Capitaine, C. Donati-Martin, and D. Féral · 2009
Earlier work this paper cites.
On Consistency and Sparsity for Principal Components Analysis in High Dimensions
I. Johnstone, and A. Lu · 2009
Earlier work this paper cites.
Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
A. Lytova and L. Pastur · 2009
Earlier work this paper cites.
Testing Hypotheses About the Number of Factors in Large Factor Models
A. Onatski · 2009
Earlier work this paper cites.
The Annals of Statistics
M. Hallin, D. Paindaveine and T. Verdebout. Optimal rank-based testing for principal components · 2010
Earlier work this paper cites.
Fundamental limit of sample generalized eigenvalue based detection of signals in noise using relatively few signal-bearing and noise-only samples
R. R. Nadakuditi, and J. W. Silverstein · 2010
Earlier work this paper cites.
Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices
F. Benaych-Georges, A. Guionnet, and M. Maida · 2011
Earlier work this paper cites.
The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
F. Benaych-Georges, R. R. Nadakuditi · 2011
Earlier work this paper cites.
High-dimensional covariance matrix estimation in approximate factor models
J. Fan, Y. Liao, and M. Mincheva · 2011
Earlier work this paper cites.
Almost sure localization of the eigenvalues in a Gaussian information plus noise model. Application to the spiked models
P. Loubaton, P. Vallet · 2011
Cited alongside, same era.
Detection performance of Roy’s largest root test when the noise covariance matrix is arbitrary
B. Nadler and I. M. Johnstone · 2011
Cited alongside, same era.
Likelihood-Based Confidence Intervals in Exploratory Factor Analysis
F.J. Oort · 2011
Cited alongside, same era.
On sample eigenvalues in a generalized spiked population model
Z.D. Bai, J.F. Yao · 2012
Cited alongside, same era.
The singular values and vectors of low rank perturbations of large rectangular random matrices
F. Benaych-Georges, R. R. Nadakuditi · 2012
Cited alongside, same era.
Central limit theorems for eigenvalues of deformations of Wigner matrices
Outliers in the spectrum of large deformed unitarily invariant models
S. Belinschi, H. Bercovici, M. Capitaine, and M. Février · 2017
Later among the works it cites.
Cleaning large correlation matrices: Tools from Random Matrix Theory
J. Bun, J. Bouchaud, and M. Potters · 2017
Later among the works it cites.
Mesoscopic eigenvalue statistics of Wigner matrices
Y. He, A. Knowles · 2017
Later among the works it cites.
Anisotropic local laws for random matrices
A. Knowles, J. Yin · 2017
Later among the works it cites.
Sankhya A
V. Koltchinskii and K. Lounici. New asymptotic results in Principal Component Analysis · 2017
Later among the works it cites.
Limiting eigenvectors of outliers for Spiked Information-Plus-Noise type matrices
M. Capitaine · 2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
M. Capitaine, C. Donati-Martin, and D. Féral · 2012
Cited alongside, same era.
Asymptotics of the principal components estimator of large factor models with weakly influential factors
A. Onatski · 2012
Cited alongside, same era.
Principal components estimation and identification of static factors
J. Bai, and S. Ng · 2013
Cited alongside, same era.
Minimax bounds for sparse PCA with noisy high-dimensional data
A. Birnbaum, I. Johnstone, B. Nadler, and D. Paul · 2013
Cited alongside, same era.
Limits of spiked random matrices I
A. Bloemendal, B. Virág · 2013
Cited alongside, same era.
Averaging fluctuations in resolvents of random band matrices
L. Erdős, A. Knowles, and H.-T. Yau · 2013
Cited alongside, same era.
An Introduction to Statistical Learning: with Applications in R
G. James, D. Witten, T. Hastie, and R. Tibshirani · 2013
Cited alongside, same era.
M. Capitaine, C. Donati-Martin · 2018
Later among the works it cites.
Optimal shrinkage of eigenvalues in the spiked covariance model
D. Donoho, M. Gavish, and I. Johnstone · 2018
Later among the works it cites.
Notes on asymptotics of sample eigenstructure for spiked covariance models with non-Gaussian data
I. Johnstone, and J. Yang · 2018
Later among the works it cites.
Local law and Tracy-Widom limit for sparse random matrices
J. O. Lee, K. Schnelli · 2018
Later among the works it cites.
Asymptotics of eigenstructure of sample correlation matrices for high-dimensional spiked models
D. Morales-Jimenez, I. M. Johnstone, M. R. McKay, and J. Yang · 2018
Later among the works it cites.
Optimality and sub-optimality of PCA I: Spiked random matrix models
A. Perry, A.S. Wein, A.S. Bandeira, A. Moitra · 2018
Later among the works it cites.
Electronic Journal of Statistics, 12, 1948-1987, 2018
I. Silin, and V. Spokoiny. Bayesian inference for spectral projectors of the covariance matrix · 2018
Later among the works it cites.
Rank regularized estimation of approximate factor models
J. Bai, and S. Ng · 2019
Later among the works it cites.
Deterministic parallel analysis: an improved method for selecting factors and principal components
E. Dobriban and A. Owen · 2019
Later among the works it cites.
Asymptotic theory of eigenvectors for large random matrices
J. Fan, Y. Fan, X. Han, and J. Lv · 2019
Later among the works it cites.
Mesoscopic eigenvalue density correlations of Wigner matrices
Y. He, A. Knowles · 2019
Later among the works it cites.
Local law and Tracy–Widom limit for sparse sample covariance matrices
J. Hwang, J. Lee, and K. Schnelli · 2019
Later among the works it cites.
Bootstrap confidence sets for spectral projectors of sample covariance
A. Naumov, V. Spokoiny, and V. Ulyanov · 2019
Later among the works it cites.
Singular vector and singular subspace distribution for the matrix denoising model
Z.G. Bao, X.C. Ding, and K. Wang · 2020
Closest in time.
High dimensional deformed rectangular matrices with applications in matrix denoising
X.C. Ding · 2020
Closest in time.
Spiked separable covariance matrices and principal components
X.C. Ding, F. Yang · 2020
Closest in time.
Permutation methods for factor analysis and PCA
E. Dobriban · 2020
Closest in time.
Estimation of the number of spiked eigenvalues in a covariance matrix by bulk eigenvalue matching analysis
Z. Ke, Y. Ma, and X. Lin · 2020
Closest in time.
Asymptotic joint distribution of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model
Z. Li, F. Han, and J. Yao · 2020
Closest in time.
Hypothesis testing for eigenspaces of covariance matrix
I. Silin, and J. Fan · 2020
Closest in time.
Convergence of eigenvector empirical spectral distribution of sample covariance matrices
H.K. Xi, F. Yang, J. Yin · 2020
Closest in time.