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

DOI10.3150/10-BEJ334zbMath1248.60010arXiv1203.0839MaRDI QIDQ408106

Zongming Ma

Publication date: 29 March 2012

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.0839

zbMATH Keywords

rate of convergenceprincipal component analysisrandom matricesWishart distributionTracy-Widom distributionLaguerre ensemble

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Random matrices (probabilistic aspects) (60B20)

Related Items (23)

Eigenvalues and eigenvectors of heavy-tailed sample covariance matrices with general growth rates: the iid case ⋮ On the Tracy-Widom approximation of Studentized extreme eigenvalues of Wishart matrices ⋮ Goodness-of-fit test for latent block models ⋮ Convergence rate to the Tracy-Widom laws for the largest eigenvalue of Wigner matrices ⋮ Functional form for the leading correction to the distribution of the largest eigenvalue in the GUE and LUE ⋮ Approximation of rectangular beta-Laguerre ensembles and large deviations ⋮ Convergence rate to the Tracy-Widom laws for the largest eigenvalue of sample covariance matrices ⋮ Behavior of Some Hypothesis Tests for the Covariance Matrix of High Dimensional Data ⋮ On randomized sketching algorithms and the Tracy-Widom law ⋮ Limiting distribution of maximal crossing and nesting of Poissonized random matchings ⋮ Optimal soft edge scaling variables for the Gaussian and Laguerre even \(\beta\) ensembles ⋮ Random matrix theory in statistics: a review ⋮ Asymptotic correlations with corrections for the circular Jacobi \(\beta\)-ensemble ⋮ Estimating tail probabilities of the ratio of the largest eigenvalue to the trace of a Wishart matrix ⋮ Asymptotic joint distribution of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model ⋮ Recursion for the smallest eigenvalue density of \(\beta \)-Wishart-Laguerre ensemble ⋮ Fast approach to the tracy-widom law at the edge of GOE and GUE ⋮ Roy's largest root under rank-one perturbations: the complex valued case and applications ⋮ Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution ⋮ Tracy-Widom limit for Kendall's tau ⋮ Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence ⋮ Estimating structured high-dimensional covariance and precision matrices: optimal rates and adaptive estimation ⋮ Tracy-Widom at each edge of real covariance and MANOVA estimators

Uses Software

• Rmtstat

Cites Work

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• On a Heuristic Method of Test Construction and its use in Multivariate Analysis
• Traces and determinants of linear operators

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