On a distributional bound arising in autoregressive model fitting

1994 ◽  
Vol 31 (2) ◽  
pp. 401-408 ◽  
Author(s):  
F. Papangelou
Keyword(s):  
Autoregressive Model ◽  
Infinite Order ◽  
Model Fitting ◽  
Uniform Boundedness ◽  
Covariance Matrices ◽  
Large Sample Size ◽  
Ergodic Theorems ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Special Case

In the theory of autoregressive model fitting it is of interest to know the asymptotic behaviour, for large sample size, of the coefficients fitted. A significant role is played in this connection by the moments of the norms of the inverse sample covariance matrices. We establish uniform boundedness results for these, first under generally weak conditions and then for the special case of (infinite order) processes. These in turn imply corresponding ergodic theorems for the matrices in question.

On a distributional bound arising in autoregressive model fitting

1994 ◽  
Vol 31 (02) ◽  
pp. 401-408
Author(s):  
F. Papangelou
Keyword(s):  
Autoregressive Model ◽  
Infinite Order ◽  
Model Fitting ◽  
Uniform Boundedness ◽  
Covariance Matrices ◽  
Large Sample Size ◽  
Ergodic Theorems ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Special Case

In the theory of autoregressive model fitting it is of interest to know the asymptotic behaviour, for large sample size, of the coefficients fitted. A significant role is played in this connection by the moments of the norms of the inverse sample covariance matrices. We establish uniform boundedness results for these, first under generally weak conditions and then for the special case of (infinite order) processes. These in turn imply corresponding ergodic theorems for the matrices in question.

scholarly journals Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices Generated by the Periodic Autoregressive Model

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jin Zou ◽  
Dong Han
Keyword(s):  
Spectral Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Autoregressive Model ◽  
Spectral Density Function ◽  
Entropy Method ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
The Moment

The explicit representation for the limiting spectral moments of sample covariance matrices generated by the periodic autoregressive model (PAR) is established. We propose to use the moment-constrained maximum entropy method to estimate the spectral density function. The experiments show that the maximum entropy spectral density function curve obtained based on the fourth-order limiting spectral moment can match histograms of the eigenvalues of the covariance matrices very well.

scholarly journals On the principal components of sample covariance matrices

2015 ◽  
Vol 164 (1-2) ◽  
pp. 459-552 ◽  
Author(s):  
Alex Bloemendal ◽  
Antti Knowles ◽  
Horng-Tzer Yau ◽  
Jun Yin
Keyword(s):  
Principal Components ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance

Some strong convergence theorems for eigenvalues of general sample covariance matrices

2021 ◽  
Author(s):  
Yanqing Yin
Keyword(s):  
General Population ◽  
Strong Convergence ◽  
Spectral Properties ◽  
Closed Interval ◽  
Open Interval ◽  
Convergence Result ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Class Of Matrices

The aim of this paper is to investigate the spectral properties of sample covariance matrices under a more general population. We consider a class of matrices of the form [Formula: see text], where [Formula: see text] is a [Formula: see text] nonrandom matrix and [Formula: see text] is an [Formula: see text] matrix consisting of i.i.d standard complex entries. [Formula: see text] as [Formula: see text] while [Formula: see text] can be arbitrary but no smaller than [Formula: see text]. We first prove that under some mild assumptions, with probability 1, for all large [Formula: see text], there will be no eigenvalues in any closed interval contained in an open interval which is outside the supports of the limiting distributions for all sufficiently large [Formula: see text]. Then we get the strong convergence result for the extreme eigenvalues as an extension of Bai-Yin law.

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