Concentration of measure and spectra of random matrices: applications to correlation matrices, elliptical distributions and beyond

DOI10.1214/08-AAP548zbMath1255.62156arXiv0912.1950OpenAlexW3099134300MaRDI QIDQ1049567

Noureddine El Karoui

Publication date: 13 January 2010

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

Full work available at URL: https://arxiv.org/abs/0912.1950

zbMATH Keywords

multivariate statistical analysishigh-dimensional inferencecovariance matriceseigenvalues of covariance matrices

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Applications of statistics to economics (62P20) Asymptotic distribution theory in statistics (62E20) Measures of association (correlation, canonical correlation, etc.) (62H20) Random matrices (algebraic aspects) (15B52)

Related Items

Spectral Properties of Rescaled Sample Correlation Matrix, Controlling the least eigenvalue of a random Gram matrix, Asymptotics for high dimensional regression \(M\)-estimates: fixed design results, Marčenko-Pastur law for Tyler's M-estimator, Limiting Spectral Distribution for Large Sample Covariance Matrices with Graph-Dependent Elements, Kernel spectral clustering of large dimensional data, Learning curves of generic features maps for realistic datasets with a teacher-student model*, Almost sure convergence of the largest and smallest eigenvalues of high-dimensional sample correlation matrices, The spectrum of kernel random matrices, Limiting spectral distribution of large dimensional Spearman's rank correlation matrices, A random matrix approach to neural networks, On information plus noise kernel random matrices, On the Spectrum of Sample Covariance Matrices for Time Series, Tracy-Widom limit for the largest eigenvalue of high-dimensional covariance matrices in elliptical distributions, Marchenko–Pastur law with relaxed independence conditions, High-dimensionality effects in the Markowitz problem and other quadratic programs with linear constraints: risk underestimation, On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence, Marchenko-Pastur law for a random tensor model, Convergence of eigenvector empirical spectral distribution of sample covariance matrices, A bootstrap method for spectral statistics in high-dimensional elliptical models, Logarithmic law of large random correlation matrices, Spectral convergence for a general class of random matrices, Graph connection Laplacian and random matrices with random blocks, Central limit theorem of linear spectral statistics of high-dimensional sample correlation matrices, Detecting approximate replicate components of a high-dimensional random vector with latent structure, Most powerful test against a sequence of high dimensional local alternatives, Limiting spectral distribution of renormalized separable sample covariance matrices when \(p/n\to 0\), Random matrix theory in statistics: a review, Distribution of eigenvalues of large Euclidean matrices generated from \(l_p\) ellipsoid, High-dimensional covariance matrices in elliptical distributions with application to spherical test, From Fixed-X to Random-X Regression: Bias-Variance Decompositions, Covariance Penalties, and Prediction Error Estimation, Point process convergence for the off-diagonal entries of sample covariance matrices, On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators, On the inference about the spectral distribution of high-dimensional covariance matrix based on high-frequency noisy observations, Cleaning large correlation matrices: tools from random matrix theory, Can we trust the bootstrap in high-dimension?, Edge universality of separable covariance matrices, Graph connection Laplacian methods can be made robust to noise, High-dimensional sample covariance matrices with Curie-Weiss entries, On the singular value distribution of large-dimensional data matrices whose columns have different correlations, SOME REMARKS ON THE DOZIER–SILVERSTEIN THEOREM FOR RANDOM MATRICES WITH DEPENDENT ENTRIES, Stochastic orderings of multivariate elliptical distributions, Large sample correlation matrices: a comparison theorem and its applications, Asymptotics of eigenstructure of sample correlation matrices for high-dimensional spiked models, THE SPECTRUM OF RANDOM KERNEL MATRICES: UNIVERSALITY RESULTS FOR ROUGH AND VARYING KERNELS, Universality for the largest eigenvalue of sample covariance matrices with general population, On the Marčenko-Pastur law for linear time series, Properties of eigenvalues and eigenvectors of large-dimensional sample correlation matrices, Limiting distributions for eigenvalues of sample correlation matrices from heavy-tailed populations

Uses Software

• QRM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A well-conditioned estimator for large-dimensional covariance matrices
• A CLT for a band matrix model
• An introduction to copulas.
• The spectrum of kernel random matrices
• No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix
• Spectrum estimation for large dimensional covariance matrices using random matrix theory
• Statistical eigen-inference from large Wishart matrices
• On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
• A limit theorem for the norm of random matrices
• Some limit theorems for the eigenvalues of a sample covariance matrix
• No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
• Concentration of the spectral measure for large matrices
• On the distribution of the largest eigenvalue in principal components analysis
• Necessary and sufficient condition that the limit of Stieltjes transforms is a Stieltjes transform
• CLT for linear spectral statistics of large-dimensional sample covariance matrices.
• On the empirical distribution of eigenvalues of a class of large dimensional random matrices
• Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices
• Concentration of measure and isoperimetric inequalities in product spaces
• The spectrum edge of random matrix ensembles.
• Shape fluctuations and random matrices
• Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
• Regularized estimation of large covariance matrices
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution
• Design of Reduced-Rank MMSE Multiuser Detectors Using Random Matrix Methods
• Asymptotic Statistics
• RANDOM MATRIX THEORY AND FINANCIAL CORRELATIONS
• Random Matrix Theory and Wireless Communications