Some strong limit theorems for the largest entries of sample correlation matrices

DOI10.1214/105051605000000773zbMath1098.60034arXivmath/0603334OpenAlexW1975925591MaRDI QIDQ2494587

Andrew Rosalsky, De Li Li

Publication date: 29 June 2006

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

Full work available at URL: https://arxiv.org/abs/math/0603334

Mathematics Subject Classification ID

Strong limit theorems (60F15)

Related Items (18)

Central limit theorems for classical likelihood ratio tests for high-dimensional normal distributions ⋮ Phase transition in limiting distributions of coherence of high-dimensional random matrices ⋮ Strong limit theorem for largest entry of large-dimensional random tensor ⋮ Extremes of weighted Brownian bridges in increasing dimension ⋮ Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices ⋮ Limiting behavior of largest entry of random tensor constructed by high-dimensional data ⋮ On Jiang's asymptotic distribution of the largest entry of a sample correlation matrix ⋮ A Darling-Erdős type result for stationary ellipsoids ⋮ Necessary and sufficient conditions for the asymptotic distributions of coherence of ultra-high dimensional random matrices ⋮ Asymptotic theory for maximum deviations of sample covariance matrix estimates ⋮ Point process convergence for the off-diagonal entries of sample covariance matrices ⋮ Largest entries of sample correlation matrices from equi-correlated normal populations ⋮ Necessary and sufficient conditions for the asymptotic distribution of the largest entry of a sample correlation matrix ⋮ The entries of circular orthogonal ensembles ⋮ Asymptotic analysis for extreme eigenvalues of principal minors of random matrices ⋮ Asymptotic distribution of the maximum interpoint distance for high-dimensional data ⋮ Large sample correlation matrices: a comparison theorem and its applications ⋮ The asymptotic distributions of the largest entries of sample correlation matrices under an \(\alpha\)-mixing assumption

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• The asymptotic distributions of the largest entries of sample correlation matrices.
• Convergence Rates in the Law of Large Numbers
• Sums of independent Banach space valued random variables

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