On singular values distribution of a matrix large auto-covariance in the ultra-dimensional regime

DOI10.1142/S201032631550015XzbMath1330.15044arXiv1501.06641OpenAlexW3101385534MaRDI QIDQ3459155

Qinwen Wang, Jian-feng Yao

Publication date: 30 December 2015

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.06641

zbMATH Keywords

largest eigenvaluesingular valueslimiting spectral distributionmoment methodauto-covariance matrixsingular value distributionultra-dimensional data

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Strong limit theorems (60F15) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

Related Items (3)

The Tracy-Widom law for the largest eigenvalue of F type matrices ⋮ Large sample autocovariance matrices of linear processes with heavy tails ⋮ Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by VARMA

Cites Work

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• Strong limit of the extreme eigenvalues of a symmetrized auto-cross covariance matrix
• Spectral analysis of large dimensional random matrices
• Convergence to the semicircle law
• Convergence of the largest eigenvalue of normalized sample covariance matrices when \(p\) and \(n\) both tend to infinity with their ratio converging to zero
• On singular value distribution of large-dimensional autocovariance matrices
• Limiting spectral distribution of renormalized separable sample covariance matrices when \(p/n\to 0\)
• Limiting spectral distribution of a symmetrized auto-cross covariance matrix

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