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English	Random matrix theory in statistics: a review	scientific article

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scholarly article

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Random matrix theory in statistics: a review (English)

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Journal of Statistical Planning and Inference

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publication date

10 June 2014

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full work available at URL

https://escholarship.org/uc/item/2350x9hz

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zbMATH Keywords

MANOVA

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Marčenko-Pastur law

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principal components analysis

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Stieltjes transforms

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Wishart matrix

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Tracy-Widom law

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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High-dimensional analysis of semidefinite relaxations for sparse principal components

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A CLT for a band matrix model

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On the asymptotic distribution of the eigenvalues of random matrices

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On Wigner's semicircle law for the eigenvalues of random matrices

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Poisson convergence for the largest eigenvalues of heavy tailed random matrices

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Inferential Theory for Factor Models of Large Dimensions

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Determining the Number of Factors in Approximate Factor Models

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Convergence rate of expected spectral distributions of large random matrices. I: Wigner matrices

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Convergence rate of expected spectral distributions of large random matrices. II: Sample covariance matrices

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ON ESTIMATION OF THE POPULATION SPECTRAL DISTRIBUTION FROM A HIGH‐DIMENSIONAL SAMPLE COVARIANCE MATRIX

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Convergence of the empirical spectral distribution function of beta matrices

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Corrections to LRT on large-dimensional covariance matrix by RMT

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Asymptotic properties of eigenmatrices of a large sample covariance matrix

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On asymptotics of eigenvectors of large sample covariance matrix

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A note on the convergence rate of the spectral distributions of large random matrices

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Remarks on the convergence rate of the spectral distributions of Wigner matrices

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Convergence Rates of Spectral Distributions of Large Sample Covariance Matrices

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No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices

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Exact separation of eigenvalues of large dimensional sample covariance matrices

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CLT for linear spectral statistics of large-dimensional sample covariance matrices.

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On the signal-to-interference ratio of CDMA systems in wireless communications

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NO EIGENVALUES OUTSIDE THE SUPPORT OF THE LIMITING SPECTRAL DISTRIBUTION OF INFORMATION-PLUS-NOISE TYPE MATRICES

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A note on the largest eigenvalue of a large dimensional sample covariance matrix

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CLT for linear spectral statistics of Wigner matrices

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Functional CLT for sample covariance matrices

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On the convergence of the spectral empirical process of Wigner matrices

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On sample eigenvalues in a generalized spiked population model

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Convergence to the semicircle law

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Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix

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Limit of the smallest eigenvalue of a large dimensional sample covariance matrix

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Semicircle Law for Hadamard Products

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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices

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Eigenvalues of large sample covariance matrices of spiked population models

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Random matrix ensembles with an effective extensive external charge

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Strong convergence of ESD for the generalized sample covariance matrices when \(p/n \rightarrow 0\)

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Tracy-Widom law for the extreme eigenvalues of sample correlation matrices

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Universality of local eigenvalue statistics for some sample covariance matrices

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Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices

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Large deviations of the extreme eigenvalues of random deformations of matrices

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The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices

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Performance of Statistical Tests for Single-Source Detection Using Random Matrix Theory

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Some theory for Fisher's linear discriminant function, `naive Bayes', and some alternatives when there are many more variables than observations

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Covariance regularization by thresholding

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Regularized estimation of large covariance matrices

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Minimax bounds for sparse PCA with noisy high-dimensional data

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On the top eigenvalue of heavy-tailed random matrices

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Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws

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Another look at the moment method for large dimensional random matrices

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Theory of Financial Risk and Derivative Pricing

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Spectral measure of large random Hankel, Markov and Toeplitz matrices

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Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices

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Adaptive Thresholding for Sparse Covariance Matrix Estimation

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A Direct Estimation Approach to Sparse Linear Discriminant Analysis

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A Constrained<i>ℓ</i><sub>1</sub>Minimization Approach to Sparse Precision Matrix Estimation

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Sparse PCA: optimal rates and adaptive estimation

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Adaptive covariance matrix estimation through block thresholding

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Optimal rates of convergence for covariance matrix estimation

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The largest eigenvalues of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations

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The outliers among the singular values of large rectangular random matrices with additive fixed rank deformation

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A generalization of the Lindeberg principle

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Fluctuations of eigenvalues and second order Poincaré inequalities

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On a model selection problem from high-dimensional sample covariance matrices

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A Regularized Hotelling’s<i>T</i><sup>2</sup>Test for Pathway Analysis in Proteomic Studies

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A two-sample test for high-dimensional data with applications to gene-set testing

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Edgeworth expansion of the largest eigenvalue distribution function of GUE and LUE

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Random Matrix Methods for Wireless Communications

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Eigen-Inference for Energy Estimation of Multiple Sources

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A Direct Formulation for Sparse PCA Using Semidefinite Programming

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Limit theory for the largest eigenvalues of sample covariance matrices with heavy-tails

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Estimation of a covariance matrix under Stein's loss

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Trimmed minimax estimator of a covariance matrix

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Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture

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Linear functionals of eigenvalues of random matrices

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Spectral distributions of adjacency and Laplacian matrices of random graphs

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Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices

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On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices

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Matrix models for beta ensembles

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Statistical Theory of the Energy Levels of Complex Systems. I

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Random matrix theory

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From random matrices to stochastic operators

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Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices

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Operator norm consistent estimation of large-dimensional sparse covariance matrices

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Spectrum estimation for large dimensional covariance matrices using random matrix theory

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

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On the Realized Risk of High-Dimensional Markowitz Portfolios

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High-dimensionality effects in the Markowitz problem and other quadratic programs with linear constraints: risk underestimation

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On information plus noise kernel random matrices

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The spectrum of kernel random matrices

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Bulk universality for Wigner matrices

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Bulk universality for Wigner Hermite matrices with subexponential decay

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Local semicircle law and complete delocalization for Wigner random matrices

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Universality of local spectral statistics of random matrices

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Rigidity of eigenvalues of generalized Wigner matrices

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High-dimensional classification using features annealed independence rules

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A universality result for the smallest eigenvalues of certain sample covariance matrices

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The largest eigenvalue of rank one deformation of large Wigner matrices

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

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The generalized dynamic factor model consistency and rates

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The Generalized Dynamic Factor Model

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Sparse inverse covariance estimation with the graphical lasso

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A limit theorem for the norm of random matrices

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Necessary and sufficient condition that the limit of Stieltjes transforms is a Stieltjes transform

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Interpolation zwischen den Klassen 𝔖<sub><i>p</i></sub> von Operatoren in Hilberträumen

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Rate of convergence to the semi-circular law

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Rate of convergence in probability to the Marchenko-Pastur law

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An Analysis of a Two-Way Model with Interaction and No Replication

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Large random matrices: Lectures on macroscopic asymptotics. École d'Été des Probabilités de Saint-Flour XXXVI -- 2006

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Concentration of the spectral measure for large matrices

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Gaussian fluctuations of eigenvalues in the GUE

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A CLT FOR INFORMATION-THEORETIC STATISTICS OF NON-CENTERED GRAM RANDOM MATRICES

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LARGE INFORMATION PLUS NOISE RANDOM MATRIX MODELS AND CONSISTENT SUBSPACE ESTIMATION IN LARGE SENSOR NETWORKS

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A subspace estimator for fixed rank perturbations of large random matrices

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The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile

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Deterministic equivalents for certain functionals of large random matrices

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A CLT for information-theoretic statistics of Gram random matrices with a given variance profile

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Minimax estimators for a multinormal precision matrix

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Empirical Bayes estimation of the multivariate normal covariance matrix

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Explaining the single factor bias of arbitrage pricing models in finite samples

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Sparse canonical correlation analysis

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Robust Estimation of a Location Parameter

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Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles

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Low eigenvalues of Laplacian matrices of large random graphs

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Limiting spectral distribution of large-dimensional sample covariance matrices generated by VARMA

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On fluctuations of eigenvalues of random Hermitian matrices.

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Shape fluctuations and random matrices

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Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices

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On the distribution of the largest eigenvalue in principal components analysis

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Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence

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Approximate null distribution of the largest root in multivariate analysis

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On Consistency and Sparsity for Principal Components Analysis in High Dimensions

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Fast approach to the tracy-widom law at the edge of GOE and GUE

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Principal component analysis.

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Some limit theorems for the eigenvalues of a sample covariance matrix

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Asymptotic properties of large random matrices with independent entries

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The Isotropic Semicircle Law and Deformation of Wigner Matrices

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The outliers of a deformed Wigner matrix

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Sparsistency and rates of convergence in large covariance matrix estimation

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Eigenvectors of some large sample covariance matrix ensembles

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Nonlinear shrinkage estimation of large-dimensional covariance matrices

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Estimating covariance matrices

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Central limit theorem for linear eigenvalue statistics of random matrices with independent entries

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Accuracy of the Tracy-Widom limits for the extreme eigenvalues in white Wishart matrices

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Sparse principal component analysis and iterative thresholding

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Robust m-estimators of multivariate location and scatter

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DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES

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High-dimensional graphs and variable selection with the Lasso

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Improved Estimation of Eigenvalues and Eigenvectors of Covariance Matrices Using Their Sample Estimates

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Second order freeness and fluctuations of random matrices. I: Gaussian and Wishart matrices and cyclic Fock spaces

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Finite sample approximation results for principal component analysis: A matrix perturbation approach

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On the distribution of the ratio of the largest eigenvalue to the trace of a Wishart matrix

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Random matrices: law of the determinant

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Lectures on the Combinatorics of Free Probability

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Testing Hypotheses About the Number of Factors in Large Factor Models

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Asymptotics of the principal components estimator of large factor models with weakly influential factors

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Gaussian fluctuations of eigenvalues in Wigner random matrices

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On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries

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Central limit theorem for Hotelling's \(T^{2}\) statistic under large dimension

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Sparse Canonical Correlation Analysis with Application to Genomic Data Integration

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No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix

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Universality results for the largest eigenvalues of some sample covariance matrix ensembles

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On the lower bound of the spectral norm of symmetric random matrices with independent entries

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Partial Correlation Estimation by Joint Sparse Regression Models

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Eigenvalue distribution of large sample covariance matrices of linear processes

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Edge universality of correlation matrices

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On finite rank deformations of Wigner matrices

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Beta ensembles, stochastic Airy spectrum, and a diffusion

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Statistical eigen-inference from large Wishart matrices

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A Gaussian scenario for unsupervised learning

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ON FINITE RANK DEFORMATIONS OF WIGNER MATRICES II: DELOCALIZED PERTURBATIONS

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Spectral clustering and the high-dimensional stochastic blockmodel

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Sparse permutation invariant covariance estimation

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Generalized Thresholding of Large Covariance Matrices

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On a Heuristic Method of Test Construction and its use in Multivariate Analysis

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Sparse linear discriminant analysis by thresholding for high dimensional data

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Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices

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Some limit theorems on the eigenvectors of large dimensional sample covariance matrices

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The Limiting Eigenvalue Distribution of a Multivariate <i>F</i> Matrix

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Weak convergence of random functions defined by the eigenvectors of sample covariance matrices

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On the empirical distribution of eigenvalues of a class of large dimensional random matrices

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Central limit theorem for traces of large random symmetric matrices with independent matrix elements

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Random matrices, nonbacktracking walks, and orthogonal polynomials

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The Tracy-Widom law for some sparse random matrices

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The spectral edge of some random band matrices

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Universality at the edge of the spectrum in Wigner random matrices.

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Determinantal random point fields

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Gaussian limit for determinantal random point fields.

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A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices

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Poisson statistics for the largest eigenvalues of Wigner random matrices with heavy tails

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Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles

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A test for the mean vector with fewer observations than the dimension

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Random matrices: The distribution of the smallest singular values

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Random matrices: Universality of local eigenvalue statistics up to the edge

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Random matrices: universality of local eigenvalue statistics

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A central limit theorem for the determinant of a Wigner matrix

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Random covariance matrices: universality of local statistics of eigenvalues

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RANDOM MATRICES: SHARP CONCENTRATION OF EIGENVALUES

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Probabilistic Principal Component Analysis

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Fredholm determinants, differential equations and matrix models

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Level-spacing distributions and the Airy kernel

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On orthogonal and symplectic matrix ensembles

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Spectral norm of products of random and deterministic matrices

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The strong limits of random matrix spectra for sample matrices of independent elements

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The limiting empirical measure of multiple discriminant ratios

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RANDOM COVARIANCE MATRICES: UNIVERSALITY OF LOCAL STATISTICS OF EIGENVALUES UP TO THE EDGE

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Optimal unsupervised learning

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On the relation between orthogonal, symplectic and unitary matrix ensembles

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Characteristic vectors of bordered matrices with infinite dimensions

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On the distribution of the roots of certain symmetric matrices

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Covariance-Regularized Regression and Classification for high Dimensional Problems

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Penalized Classification using Fisher’s Linear Discriminant

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A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis

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Nonparametric estimation of large covariance matrices of longitudinal data

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The convergence of the empirical distribution of canonical correlation coefficients

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A note on a Marčenko-Pastur type theorem for time series

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Limiting spectral distribution for a class of random matrices

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Limiting behavior of the eigenvalues of a multivariate F matrix

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On the limit of the largest eigenvalue of the large dimensional sample covariance matrix

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A limit theorem for the eigenvalues of product of two random matrices

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Model selection and estimation in the Gaussian graphical model

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Central limit theorems for linear spectral statistics of large dimensional \(F\)-matrices

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On the estimation of integrated covariance matrices of high dimensional diffusion processes

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Identifiers

zbMATH Open document ID

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10.1016/j.jspi.2013.09.005

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2453609

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