Universality for the largest eigenvalue of sample covariance matrices with general population

DOI10.1214/14-AOS1281zbMath1408.60006arXiv1304.5690MaRDI QIDQ2338931

Wang Zhou, Guangming Pan, Zhigang Bao

Publication date: 27 March 2015

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.5690

zbMATH Keywords

sample covariance matricesTracy-Widom lawedge universality

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Factor analysis and principal components; correspondence analysis (62H25) Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Limits of spiked random matrices. I
• Asymptotic power of sphericity tests for high-dimensional data
• The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source. I
• Random covariance matrices: universality of local statistics of eigenvalues
• Tracy-Widom law for the extreme eigenvalues of sample correlation matrices
• Random matrices: universality of local eigenvalue statistics
• Universality of random matrices and local relaxation flow
• Universality for generalized Wigner matrices with Bernoulli distribution
• Rigidity of eigenvalues of generalized Wigner matrices
• Edge universality of correlation matrices
• Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues
• Local semicircle law and complete delocalization for Wigner random matrices
• Central limit theorems for eigenvalues in a spiked population model
• No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix
• Universality results for the largest eigenvalues of some sample covariance matrix ensembles
• Spectral analysis of large dimensional random matrices
• Concentration of measure and spectra of random matrices: applications to correlation matrices, elliptical distributions and beyond
• Level-spacing distributions and the Airy kernel
• A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
• On the distribution of the largest eigenvalue in principal components analysis
• Analysis of the limiting spectral distribution of large dimensional random matrices
• On orthogonal and symplectic matrix ensembles
• Bulk universality for generalized Wigner matrices
• Shape fluctuations and random matrices
• Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
• Universality for the largest eigenvalue of sample covariance matrices with general population
• Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
• The Tracy-Widom limit for the largest eigenvalues of singular complex Wishart matrices
• The local relaxation flow approach to universality of the local statistics for random matrices
• Limiting spectral distribution of renormalized separable sample covariance matrices when \(p/n\to 0\)
• A necessary and sufficient condition for edge universality of Wigner matrices
• Universality of covariance matrices
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• Detection of discontinuous signals for cognitive radio applications
• RANDOM COVARIANCE MATRICES: UNIVERSALITY OF LOCAL STATISTICS OF EIGENVALUES UP TO THE EDGE
• The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case
• Universality of Wigner random matrices: a survey of recent results
• Rank 1 real Wishart spiked model
• Testing Hypotheses About the Number of Factors in Large Factor Models
• Sample Eigenvalue Based Detection of High-Dimensional Signals in White Noise Using Relatively Few Samples
• Statistical Inference in Large Antenna Arrays Under Unknown Noise Pattern
• Wegner Estimate and Level Repulsion for Wigner Random Matrices
• Performance of Statistical Tests for Single-Source Detection Using Random Matrix Theory
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
• ON THE DISTRIBUTION OF ROOTS OF CERTAIN DETERMINANTAL EQUATIONS
• THE SAMPLING DISTRIBUTION OF SOME STATISTICS OBTAINED FROM NON‐LINEAR EQUATIONS

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