CLT for linear spectral statistics of a rescaled sample precision matrix

DOI10.1142/S2010326315500148zbMath1330.15045OpenAlexW2239721068MaRDI QIDQ3459154

Shurong Zheng, Zhi-Dong Bai, Jian-feng Yao

Publication date: 30 December 2015

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s2010326315500148

zbMATH Keywords

central limit theoremrandom matrixmultivariate statistical analysisprecision matrixcovariance matricesFisher matrixlinear spectral statisticsrescaled precision matrix

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52) Analysis of variance and covariance (ANOVA) (62J10)

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Spectral analysis of the Moore-Penrose inverse of a large dimensional sample covariance matrix, Fluctuations of the diagonal entries of a large sample precision matrix, Limiting spectral distribution of high-dimensional noncentral Fisher matrices and its analysis, Testing covariance structure of large-dimensional data based on Wald’s score test, On the limit of the spectral distribution of large-dimensional random quaternion covariance matrices, Testing for independence of large dimensional vectors

Cites Work

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• A new test for the proportionality of two large-dimensional covariance matrices
• On the singular spectrum of powers and products of random matrices
• Central limit theorem for linear eigenvalue statistics of the Wigner and the sample covariance random matrices
• On the convergence of the spectral empirical process of Wigner matrices
• Second order freeness and fluctuations of random matrices. II: Unitary random matrices
• Central limit theorem for signal-to-interference ratio of reduced rank linear receiver
• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• Spectral analysis of large dimensional random matrices
• Corrections to LRT on large-dimensional covariance matrix by RMT
• The limiting empirical measure of multiple discriminant ratios
• Some limit theorems for the eigenvalues of a sample covariance matrix
• CLT for linear spectral statistics of large-dimensional sample covariance matrices.
• Testing the independence of sets of large-dimensional variables
• On fluctuations of eigenvalues of random Hermitian matrices.
• Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing
• Random matrix theory in statistics: a review
• Multiplication of free random variables and the \(S\)-transform: the case of vanishing mean
• Second order freeness and fluctuations of random matrices. I: Gaussian and Wishart matrices and cyclic Fock spaces
• Testing linear hypotheses in high-dimensional regressions
• Free Random Variables
• The Limiting Eigenvalue Distribution of a Multivariate F Matrix