Extreme eigenvalues of large dimensional quaternion sample covariance matrices

DOI10.1016/j.jspi.2014.10.005zbMath1311.60036arXiv1312.4649OpenAlexW2962897255MaRDI QIDQ2343830

Huiqin Li, Zhi-Dong Bai

Publication date: 6 May 2015

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.4649

zbMATH Keywords

random matrix theoryextreme eigenvaluesquaternion matricessample covariance matrixlarge dimension

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Strong limit theorems (60F15) Random matrices (algebraic aspects) (15B52) Functional limit theorems; invariance principles (60F17)

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Kernel estimators for Marčenko-Pastur law of quaternion sample covariance matrices ⋮ Strong convergence of ESD for large quaternion sample covariance matrices and correlation matrices when p/n → 0 ⋮ A CLT for the LSS of large-dimensional sample covariance matrices with diverging spikes ⋮ On the limit of the spectral distribution of large-dimensional random quaternion covariance matrices ⋮ Central limit theorem for linear spectral statistics of large dimensional quaternion sample covariance matrices ⋮ No eigenvalues outside the support of the limiting spectral distribution of quaternion sample covariance matrices

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