Almost sure limit of the smallest eigenvalue of some sample correlation matrices

DOI10.1007/s10959-009-0270-2zbMath1185.62098OpenAlexW2090808114MaRDI QIDQ966514

Han Xiao, Wang Zhou

Publication date: 23 April 2010

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-009-0270-2

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Multivariate analysis (62H99) Strong limit theorems (60F15) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items

Spectral Properties of Rescaled Sample Correlation Matrix ⋮ Almost sure convergence of the largest and smallest eigenvalues of high-dimensional sample correlation matrices ⋮ Central limit theorem of linear spectral statistics of high-dimensional sample correlation matrices ⋮ Central limit theorem for Hotelling's \(T^{2}\) statistic under large dimension ⋮ Comparison between two types of large sample covariance matrices ⋮ Random matrix theory for heavy-tailed time series ⋮ Asymptotics of eigenstructure of sample correlation matrices for high-dimensional spiked models ⋮ Properties of eigenvalues and eigenvectors of large-dimensional sample correlation matrices

Cites Work

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• 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
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