Strong limit of the extreme eigenvalues of a symmetrized auto-cross covariance matrix

DOI10.1214/14-AAP1092zbMath1328.60088arXiv1312.2277OpenAlexW3105045715MaRDI QIDQ894819

Chen Wang, Baisuo Jin, K. Krishnan Nair, Matthew C. Harding, Zhi-Dong Bai

Publication date: 24 November 2015

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

Full work available at URL: https://arxiv.org/abs/1312.2277

zbMATH Keywords

Stieltjes transformrandom matrix theoryextreme eigenvaluesstrong limitlimiting spectral distributiondynamic factor analysisMarčenko-Pastur lawauto-cross covariance matrixorder detection

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Strong limit theorems (60F15) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Functional limit theorems; invariance principles (60F17)

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On singular values distribution of a matrix large auto-covariance in the ultra-dimensional regime, Large sample autocovariance matrices of linear processes with heavy tails

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