The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case

DOI10.1063/1.3155785zbMath1342.62100arXiv0812.2320OpenAlexW2032921855MaRDI QIDQ3069151

Delphine Féral, Sandrine Péché

Publication date: 24 January 2011

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.2320

zbMATH Keywords

fluctuationseigenvalues and eigenfunctionscovariance matrices

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Random graphs (graph-theoretic aspects) (05C80) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (16)

Rank 1 real Wishart spiked model ⋮ The Tracy-Widom law for the largest eigenvalue of F type matrices ⋮ Gaussian determinantal processes: A new model for directionality in data ⋮ Limits of spiked random matrices. I ⋮ Asymptotic power of sphericity tests for high-dimensional data ⋮ Optimal detection of sparse principal components in high dimension ⋮ Large-dimensional random matrix theory and its applications in deep learning and wireless communications ⋮ On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence ⋮ Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations ⋮ The spectral edge of some random band matrices ⋮ Central limit theorems for eigenvalues of deformations of Wigner matrices ⋮ Signal detection in high dimension: the multispiked case ⋮ Random matrix theory in statistics: a review ⋮ Canonical correlation coefficients of high-dimensional Gaussian vectors: finite rank case ⋮ Limiting distribution of the sample canonical correlation coefficients of high-dimensional random vectors ⋮ Universality for the largest eigenvalue of sample covariance matrices with general population

Cites Work

• Central limit theorems for eigenvalues in a spiked population model
• Characteristic vectors of bordered matrices with infinite dimensions
• Universality results for the largest eigenvalues of some sample covariance matrix ensembles
• On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
• A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge for random symmetric matrices
• Level-spacing distributions and the Airy kernel
• A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
• Universality at the edge of the spectrum in Wigner random matrices.
• On the distribution of the largest eigenvalue in principal components analysis
• On orthogonal and symplectic matrix ensembles
• Shape fluctuations and random matrices
• The Tracy-Widom limit for the largest eigenvalues of singular complex Wishart matrices
• The largest eigenvalue of rank one deformation of large Wigner matrices
• Wigner random matrices with non-symmetrically distributed entries
• Painlevé formulas of the limiting distributions for nonnull complex sample covariance matrices
• Eigenvalues of large sample covariance matrices of spiked population models
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• On the top eigenvalue of heavy-tailed random matrices
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES

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