scholarly journals Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part II. Sample Covariance Matrices

1993 ◽  
Vol 21 (2) ◽  
pp. 649-672 ◽  
Author(s):  
Z. D. Bai
Keyword(s):  
Convergence Rate ◽  
Random Matrices ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Spectral Distributions

Trimmed estimators for large dimensional sparse covariance matrices

2018 ◽  
Vol 08 (01) ◽  
pp. 1950003
Author(s):  
Guangren Yang ◽  
Xia Cui
Keyword(s):  
Convergence Rate ◽  
Covariance Matrix ◽  
Covariance Matrices ◽  
Optimal Convergence Rate ◽  
Sample Covariance Matrices ◽  
Optimal Convergence ◽  
Sample Covariance ◽  
Starting Point ◽  
Pairwise Product

In this paper, we will propose two new estimators for sparse covariance matrix. Our starting point is to make the estimator of each element of covariance matrix more robust. More precisely, we will trim the observations for each pairwise product of components of population as a first step. Then we form the sample covariance matrices based on the trimmed data. Finally, we apply the thresholding to the derived sample covariance matrices. These two new estimators will be shown to achieve the optimal convergence rate.

scholarly journals Amalgamated Free Lévy Processes as Limits of Sample Covariance Matrices

2022 ◽  
Author(s):  
G. L. Zitelli
Keyword(s):  
Lévy Processes ◽  
Matrix Theory ◽  
Free Probability ◽  
Levy Processes ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Probability Spaces ◽  
Spectral Distributions ◽  
Non Gaussian

AbstractWe prove the existence of joint limiting spectral distributions for families of random sample covariance matrices modeled on fluctuations of discretized Lévy processes. These models were first considered in applications of random matrix theory to financial data, where datasets exhibit both strong multicollinearity and non-normality. When the underlying Lévy process is non-Gaussian, we show that the limiting spectral distributions are distinct from Marčenko–Pastur. In the context of operator-valued free probability, it is shown that the algebras generated by these families are asymptotically free with amalgamation over the diagonal subalgebra. This framework is used to construct operator-valued $$^*$$ ∗ -probability spaces, where the limits of sample covariance matrices play the role of non-commutative Lévy processes whose increments are free with amalgamation.

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