The Tracy-Widom law for the largest eigenvalue of F type matrices

DOI10.1214/15-AOS1427zbMath1378.60023arXiv1506.00089OpenAlexW2963555278MaRDI QIDQ309724

Guangming Pan, Xiao Han, Bo Zhang

Publication date: 7 September 2016

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

Full work available at URL: https://arxiv.org/abs/1506.00089

zbMATH Keywords

random matricessample covariance matrixTracy-Widom distributionFisher matrix

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Asymptotic theory of functional-differential equations (34K25)

Related Items (15)

The Tracy-Widom law for the largest eigenvalue of F type matrices ⋮ Cointegration in large VARs ⋮ Sample canonical correlation coefficients of high-dimensional random vectors: Local law and Tracy–Widom limit ⋮ Exact test theory in Gaussian graphical models ⋮ Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations ⋮ Convergence rate to the Tracy-Widom laws for the largest eigenvalue of sample covariance matrices ⋮ Limiting spectral distribution of high-dimensional noncentral Fisher matrices and its analysis ⋮ Tracy-Widom law for the extreme eigenvalues of large signal-plus-noise matrices ⋮ Order determination for spiked-type models with a divergent number of spikes ⋮ Canonical correlation coefficients of high-dimensional Gaussian vectors: finite rank case ⋮ A unified matrix model including both CCA and F matrices in multivariate analysis: the largest eigenvalue and its applications ⋮ Limiting laws for extreme eigenvalues of large-dimensional spiked Fisher matrices with a divergent number of spikes ⋮ Random matrix theory and its applications ⋮ Limiting distribution of the sample canonical correlation coefficients of high-dimensional random vectors ⋮ Approximation of the power functions of Roy’s largest root test under general spiked alternatives

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