High-dimensional linear models: a random matrix perspective

DOI10.1007/s13171-020-00219-yzbMath1472.62080OpenAlexW3092043258MaRDI QIDQ2051014

Jamshid Namdari, Debashis Paul, Lili Wang

Publication date: 1 September 2021

Published in: Sankhyā. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13171-020-00219-y

zbMATH Keywords

multivariate statisticslinear modelsrandom matrix theory

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05) Random matrices (probabilistic aspects) (60B20) Analysis of variance and covariance (ANOVA) (62J10)

Uses Software

• robustbase

Cites Work

• A Significance Test for the Separation of Two Highly Multivariate Small Samples
• A High Dimensional Two Sample Significance Test
• The distribution of a statistic used for testing sphericity of normal distributions
• Estimation of Variance and Covariance Components in Linear Models
• TESTS OF SIGNIFICANCE IN MULTIVARIATE ANALYSIS
• On the Limiting Distribution of Roots of a Determinantal Equation
• Multivariate Statistics
• Robust Statistics
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear shrinkage estimation of large-dimensional covariance matrices
• Two sample tests for high-dimensional covariance matrices
• An adaptable generalization of Hotelling's $T^2$ test in high dimension
• Large sample behaviour of high dimensional autocovariance matrices
• On two simple and effective procedures for high dimensional classification of general populations
• On high-dimensional misspecified mixed model analysis in genome-wide association study
• High dimensional robust M-estimation: asymptotic variance via approximate message passing
• Optimal equivariant prediction for high-dimensional linear models with arbitrary predictor covariance
• Asymptotic power of sphericity tests for high-dimensional data
• On the sphericity test with large-dimensional observations
• Random design analysis of ridge regression
• Limiting spectral distribution of a new random matrix model with dependence across rows and columns
• Central limit theorems for linear spectral statistics of large dimensional \(F\)-matrices
• Limiting spectral distribution of large sample covariance matrices associated with a class of stationary processes
• On testing the equality of high dimensional mean vectors with unequal covariance matrices
• Flexible results for quadratic forms with applications to variance components estimation
• A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices
• Statistics for high-dimensional data. Methods, theory and applications.
• Asymptotic theory for stationary processes
• A note on a Marčenko-Pastur type theorem for time series
• Central limit theorem for Hotelling's \(T^{2}\) statistic under large dimension
• On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators
• Asymptotic expansion of the misclassification probabilities of D- and A- criteria for discrimination from two high dimensional populations using the theory of large dimensional random matrices
• On the empirical spectral distribution for matrices with long memory and independent rows
• Central limit theorem for linear eigenvalue statistics of the Wigner and the sample covariance random matrices
• Estimation and tests of significance in factor analysis
• On the distribution of the roots of certain symmetric matrices
• Limiting spectral distribution of large-dimensional sample covariance matrices generated by VARMA
• Multivariate analysis of variance with fewer observations than the dimension
• The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
• A generalization of the Lindeberg principle
• Asymptotic results in canonical discriminant analysis when the dimension is large compared to the sample size
• Fluctuations of eigenvalues and second order Poincaré inequalities
• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence
• Spectrum estimation for large dimensional covariance matrices using random matrix theory
• Spectral analysis of large dimensional random matrices
• Corrections to LRT on large-dimensional covariance matrix by RMT
• Asymptotic behavior of M estimators of p regression parameters when \(p^ 2/n\) is large. II: Normal approximation
• On limiting spectral distribution of product of two random matrices when the underlying distribution is isotropic
• Estimation of parameters in a linear model
• Asymptotic expansions of the distributions of the latent roots and the latent vector of the Wishart and multivariate F matrices
• Level-spacing distributions and the Airy kernel
• Fredholm determinants, differential equations and matrix models
• Asymptotics for high dimensional regression \(M\)-estimates: fixed design results
• High-dimensional asymptotics of prediction: ridge regression and classification
• Some theory for Fisher's linear discriminant function, `naive Bayes', and some alternatives when there are many more variables than observations
• On the relation between orthogonal, symplectic and unitary matrix ensembles
• Robust regression: Asymptotics, conjectures and Monte Carlo
• 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
• Analysis of the limiting spectral distribution of large dimensional random matrices
• Testing the independence of sets of large-dimensional variables
• Tests for multivariate analysis of variance in high dimension under non-normality
• Limiting behavior of eigenvalues in high-dimensional MANOVA via RMT
• Distributed linear regression by averaging
• High-dimensional general linear hypothesis tests via non-linear spectral shrinkage
• Joint convergence of sample autocovariance matrices when \(p/n\to 0\) with application
• Eigenvalue distributions of variance components estimators in high-dimensional random effects models
• Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing
• On the Marčenko-Pastur law for linear time series
• On the limiting spectral distribution for a large class of symmetric random matrices with correlated entries
• Spectrum estimation: a unified framework for covariance matrix estimation and PCA in large dimensions
• A two-sample test for high-dimensional data with applications to gene-set testing
• Spectral analysis of sample autocovariance matrices of a class of linear time series in moderately high dimensions
• Optimal shrinkage of eigenvalues in the spiked covariance model
• Random matrix theory in statistics: a review
• Limiting spectral distribution of a symmetrized auto-cross covariance matrix
• A test for the mean vector with fewer observations than the dimension
• A note on testing the covariance matrix for large dimension
• Regularised Manova for High-Dimensional Data
• Testing linear hypotheses in high-dimensional regressions
• On robust regression with high-dimensional predictors
• A Regularized Hotelling’sT²Test for Pathway Analysis in Proteomic Studies
• Lectures on the Combinatorics of Free Probability
• Limit Theorem for the Eigenvalues of the Sample Covariance Matrix when the Underlying Distribution is Isotropic
• SOME PROBLEMS INVOLVING LINEAR HYPOTHESES IN MULTIVARIATE ANALYSIS
• The Generalization of Student's Ratio
• Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory
• High-Dimensional Statistics
• Eigenvalue distribution of large sample covariance matrices of linear processes
• Large Sample Covariance Matrices and High-Dimensional Data Analysis
• ON ESTIMATION OF THE POPULATION SPECTRAL DISTRIBUTION FROM A HIGH‐DIMENSIONAL SAMPLE COVARIANCE MATRIX
• Roy’s largest root test under rank-one alternatives
• Nonlinear system theory: Another look at dependence
• On limiting spectral distribution of large sample covariance matrices by VARMA(p,q)
• Proximité et dualité dans un espace hilbertien
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES