Nonparametric estimate of spectral density functions of sample covariance matrices generated by VARMA models

2020 ◽  
pp. 1-10
Author(s):  
Yangchun Zhang ◽  
Jiaqi Chen ◽  
Bosen Cui ◽  
Boping Tian
Keyword(s):  
Spectral Density ◽  
Covariance Matrices ◽  
Density Functions ◽  
Nonparametric Estimate ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Spectral Density Functions

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.

A New Spectral Method for Modeling Dynamic Ice Actions

2004 ◽  
Author(s):  
Tuomo Ka¨rna¨ ◽  
Yan Qu ◽  
Walter L. Ku¨hnlein
Keyword(s):  
Dynamic Response ◽  
Spectral Density ◽  
Time Correlation ◽  
General Purpose ◽  
Density Functions ◽  
Offshore Structure ◽  
Spectral Density Functions ◽  
Ice Force ◽  
Ice Forces ◽  
Scale Data

This paper presents a method of evaluating the response of a vertical offshore structure that is subjected to dynamic ice actions. The model concerns a loading scenario where a uniform ice sheet is drifting and crushing against the structure. Full scale data obtained at the lighthouse Norstro¨msgrund is used in the derivation of a method that applies both to narrow and wide structures. A large amount of events with directly measured local forces was used to derive formulas for spectral density functions of the ice force. A non-dimensional formula that was derived for the autospectrum applies for all ice thicknesses. Coherence functions are used to define the cross-spectra of the local ice forces. The two kind of spectral density functions for local forces can be used to evaluate the spectral density of the total ice force. The method takes account of both the spatial and time correlation between the local forces. Accordingly, the model provides a tool to consider the non-simultaneous characteristics of the local ice pressures while assessing the total ice force. The model can be used in conjunction with general purpose FE programs to evaluate the dynamic response of an offshore structure.

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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