scholarly journals A note on the limiting spectral distribution of a symmetrized auto-cross covariance matrix

2015 ◽  
Vol 96 ◽  
pp. 333-340 ◽  
Author(s):  
Zhidong Bai ◽  
Chen Wang
Keyword(s):  
Covariance Matrix ◽  
Spectral Distribution ◽  
Limiting Spectral Distribution ◽  
Cross Covariance ◽  
Auto Cross Covariance

scholarly journals Limiting spectral distribution of a symmetrized auto-cross covariance matrix

2014 ◽  
Vol 24 (3) ◽  
pp. 1199-1225 ◽  
Author(s):  
Baisuo Jin ◽  
Chen Wang ◽  
Z. D. Bai ◽  
K. Krishnan Nair ◽  
Matthew Harding
Keyword(s):  
Covariance Matrix ◽  
Spectral Distribution ◽  
Limiting Spectral Distribution ◽  
Cross Covariance ◽  
Auto Cross Covariance

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

2015 ◽  
Vol 25 (6) ◽  
pp. 3624-3683
Author(s):  
Chen Wang ◽  
Baisuo Jin ◽  
Z. D. Bai ◽  
K. Krishnan Nair ◽  
Matthew Harding
Keyword(s):  
Covariance Matrix ◽  
Strong Limit ◽  
Extreme Eigenvalues ◽  
Cross Covariance ◽  
Auto Cross Covariance

Polynomial generalizations of the sample variance-covariance matrix when pn−1 → 0

2016 ◽  
Vol 05 (04) ◽  
pp. 1650014 ◽  
Author(s):  
Monika Bhattacharjee ◽  
Arup Bose
Keyword(s):  
Covariance Matrix ◽  
Random Matrices ◽  
Random Matrix ◽  
Spectral Distribution ◽  
Probability Space ◽  
Sample Variance ◽  
Limiting Spectral Distribution ◽  
Matrix Polynomials ◽  
State Formula ◽  
Variance Covariance Matrix

Let [Formula: see text] be random matrices, where [Formula: see text] are independently distributed. Suppose [Formula: see text], [Formula: see text] are non-random matrices of order [Formula: see text] and [Formula: see text] respectively. Suppose [Formula: see text], [Formula: see text] and [Formula: see text]. Consider all [Formula: see text] random matrix polynomials constructed from the above matrices of the form [Formula: see text] [Formula: see text] and the corresponding centering polynomials [Formula: see text] [Formula: see text]. We show that under appropriate conditions on the above matrices, the variables in the non-commutative ∗-probability space [Formula: see text] with state [Formula: see text] converge. We also show that the limiting spectral distribution of [Formula: see text] exists almost surely whenever [Formula: see text] and [Formula: see text] are self-adjoint. The limit can be expressed in terms of, semi-circular, circular and other families and, limits of [Formula: see text], [Formula: see text] and non-commutative limit of [Formula: see text]. Our results fully generalize the results already known for [Formula: see text].

scholarly journals Estimation of the population spectral distribution from a large dimensional sample covariance matrix

2013 ◽  
Vol 143 (11) ◽  
pp. 1887-1897 ◽  
Author(s):  
Weiming Li ◽  
Jiaqi Chen ◽  
Yingli Qin ◽  
Zhidong Bai ◽  
Jianfeng Yao
Keyword(s):  
Covariance Matrix ◽  
Spectral Distribution ◽  
Sample Covariance Matrix ◽  
Sample Covariance

scholarly journals Brown measure and asymptotic freeness of elliptic and related matrices

2019 ◽  
Vol 08 (02) ◽  
pp. 1950007
Author(s):  
Kartick Adhikari ◽  
Arup Bose
Keyword(s):  
Spectral Distribution ◽  
Limiting Spectral Distribution

We show that independent elliptic matrices converge to freely independent elliptic elements. Moreover, the elliptic matrices are asymptotically free with deterministic matrices under appropriate conditions. We compute the Brown measure of the product of elliptic elements. It turns out that this Brown measure is same as the limiting spectral distribution.

Cross-covariance matrix: Time-shifted correlations for 3D action recognition

2020 ◽  
Vol 171 ◽  
pp. 107499
Author(s):  
Jianhai Zhang ◽  
Zhiyong Feng ◽  
Yong Su ◽  
Meng Xing
Keyword(s):  
Covariance Matrix ◽  
Action Recognition ◽  
Cross Covariance
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