Edge universality of separable covariance matrices

DOI10.1214/19-EJP381zbMath1436.15042arXiv1809.04572OpenAlexW3101939483MaRDI QIDQ2279318

Fan Yang

Publication date: 12 December 2019

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.04572

zbMATH Keywords

sample covariance matrixTracy-Widom lawedge universalityseparable covariance matrix

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52)

Related Items

Joint CLT for top eigenvalues of sample covariance matrices of separable high dimensional long memory processes, Sample canonical correlation coefficients of high-dimensional random vectors: Local law and Tracy–Widom limit, Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations, Convergence rate to the Tracy-Widom laws for the largest eigenvalue of sample covariance matrices, Tracy-Widom law for the extreme eigenvalues of large signal-plus-noise matrices, Convergence of eigenvector empirical spectral distribution of sample covariance matrices, Local laws for multiplication of random matrices, Spiked separable covariance matrices and principal components, Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by VARMA, Edge statistics of large dimensional deformed rectangular matrices, Limiting distribution of the sample canonical correlation coefficients of high-dimensional random vectors

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• High dimensional covariance matrix estimation using a factor model
• Asymptotic power of sphericity tests for high-dimensional data
• Delocalization and diffusion profile for random band matrices
• Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law
• Averaging fluctuations in resolvents of random band matrices
• The local semicircle law for a general class of random matrices
• Local circular law for random matrices
• Tracy-Widom distribution for the largest eigenvalue of real sample covariance matrices with general population
• Local law for random Gram matrices
• Random matrices: universality of local eigenvalue statistics
• On the weak limit of the largest eigenvalue of a large dimensional sample covariance matrix
• Rigidity of eigenvalues of generalized Wigner matrices
• Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues
• No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix
• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence
• Concentration of measure and spectra of random matrices: applications to correlation matrices, elliptical distributions and beyond
• On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
• A note on the largest eigenvalue of a large dimensional sample covariance matrix
• Level-spacing distributions and the Airy kernel
• A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices
• Singularities of the density of states of random Gram matrices
• On the distribution of the largest eigenvalue in principal components analysis
• On orthogonal and symplectic matrix ensembles
• Random matrices: Universality of local eigenvalue statistics up to the edge
• The spectrum edge of random matrix ensembles.
• Spiked separable covariance matrices and principal components
• Convergence of eigenvector empirical spectral distribution of sample covariance matrices
• Random matrices: universality of local spectral statistics of non-Hermitian 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
• Local circular law for the product of a deterministic matrix with a random matrix
• The Tracy-Widom limit for the largest eigenvalues of singular complex Wishart matrices
• Limiting spectral distribution of renormalized separable sample covariance matrices when \(p/n\to 0\)
• Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix
• A necessary and sufficient condition for edge universality of Wigner matrices
• Isotropic local laws for sample covariance and generalized Wigner matrices
• Random matrix theory in statistics: a review
• Universality of covariance matrices
• Deterministic equivalents for certain functionals of large random matrices
• Eigenvalues of large sample covariance matrices of spiked population models
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• Testing for separability of spatial\,-\,temporal covariance functions
• On the principal components of sample covariance matrices
• The Isotropic Semicircle Law and Deformation of Wigner Matrices
• Application of Random Matrix Theory to Multivariate Statistics
• Analysis of the limiting spectral measure of large random matrices of the separable covariance type
• Testing the covariance structure of multivariate random fields
• 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
• Spectral efficiency in the wideband regime
• An overview of the estimation of large covariance and precision matrices
• Large Sample Covariance Matrices and High-Dimensional Data Analysis
• Performance of Statistical Tests for Single-Source Detection Using Random Matrix Theory
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
• Random Matrix Theory and Wireless Communications
• Geostatistical space-time models: a review