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

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

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 ma...

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Main Authors: Jin Zou, Dong Han
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/9526991
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spelling doaj-39c2f4f04535443eb5bb5f5b0e052bba2021-08-30T00:00:44ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/9526991Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices Generated by the Periodic Autoregressive ModelJin Zou0Dong Han1School of Mathematics ScienceSchool of Mathematics ScienceThe 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.http://dx.doi.org/10.1155/2021/9526991
collection DOAJ
language English
format Article
sources DOAJ
author Jin Zou
Dong Han
spellingShingle Jin Zou
Dong Han
Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices Generated by the Periodic Autoregressive Model
Journal of Mathematics
author_facet Jin Zou
Dong Han
author_sort Jin Zou
title Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices Generated by the Periodic Autoregressive Model
title_short Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices Generated by the Periodic Autoregressive Model
title_full Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices Generated by the Periodic Autoregressive Model
title_fullStr Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices Generated by the Periodic Autoregressive Model
title_full_unstemmed Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices Generated by the Periodic Autoregressive Model
title_sort limiting spectral distribution of large-dimensional sample covariance matrices generated by the periodic autoregressive model
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4785
publishDate 2021-01-01
description 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.
url http://dx.doi.org/10.1155/2021/9526991
work_keys_str_mv AT jinzou limitingspectraldistributionoflargedimensionalsamplecovariancematricesgeneratedbytheperiodicautoregressivemodel
AT donghan limitingspectraldistributionoflargedimensionalsamplecovariancematricesgeneratedbytheperiodicautoregressivemodel
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