Convergence of the largest eigenvalue of normalized sample covariance matrices when \(p\) and \(n\) both tend to infinity with their ratio converging to zero

DOI10.3150/11-BEJ381zbMath1279.60012arXiv1211.5479OpenAlexW2140455169MaRDI QIDQ1932236

Yanyan Li

Publication date: 17 January 2013

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.5479

zbMATH Keywords

random matrix theoryempirical distributionsample covariance matrixmaximum eigenvalue

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Asymptotic properties of nonparametric inference (62G20) Random matrices (probabilistic aspects) (60B20) Order statistics; empirical distribution functions (62G30) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

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Cites Work

• Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
• On the distribution of the roots of certain symmetric matrices
• Operator norm consistent estimation of large-dimensional sparse covariance matrices
• On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
• Convergence to the semicircle law
• A limit theorem for the norm of random matrices
• Some limit theorems for the eigenvalues of a sample covariance matrix
• Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
• Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous Operators

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