Strong convergence of ESD for large quaternion sample covariance matrices and correlation matrices when p/n → 0
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Published:2019-05-07
Issue:02
Volume:09
Page:2050005
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ISSN:2010-3263
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Container-title:Random Matrices: Theory and Applications
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language:en
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Short-container-title:Random Matrices: Theory Appl.
Affiliation:
1. School of Mathematics, Jilin University, 2699 Qianjin Street, Changchun City, 130012, P. R. China
Abstract
In this paper, we study the strong convergence of empirical spectral distribution (ESD) of the large quaternion sample covariance matrices and correlation matrices when the ratio of the population dimension [Formula: see text] to sample size [Formula: see text] tends to zero. We prove that the ESD of renormalized quaternion sample covariance matrices converges almost surely to the semicircle law.
Funder
Science and Technology Development Program of Jilin Province
Science and Technology Program of Jilin Educational Department during the 13th Five-Year Plan Period
National Natural Science Foundation of China
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Statistics and Probability,Algebra and Number Theory