Modeling temporally uncorrelated components of complex-valued stationary processes

A complex-valued linear mixture model is considered for discrete weakly stationary processes. Latent components of interest are recovered, which underwent a linear mixing. Asymptotic properties are studied of a classical unmixing estimator which is based on simultaneous diagonalization of the covari...

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Autores principales:	Niko Lietzén, Lauri Viitasaari, Pauliina Ilmonen
Formato:	article
Lenguaje:	EN
Publicado:	VTeX 2021
Materias:	Asymptotic theory blind source separation long-range dependency multivariate analysis noncentral limit theorems Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b0865ce34d7c4be28e5a840251abab9b
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spelling	oai:doaj.org-article:b0865ce34d7c4be28e5a840251abab9b2021-11-17T08:47:30ZModeling temporally uncorrelated components of complex-valued stationary processes10.15559/21-VMSTA1902351-60462351-6054https://doaj.org/article/b0865ce34d7c4be28e5a840251abab9b2021-11-01T00:00:00Zhttps://www.vmsta.org/doi/10.15559/21-VMSTA190https://doaj.org/toc/2351-6046https://doaj.org/toc/2351-6054A complex-valued linear mixture model is considered for discrete weakly stationary processes. Latent components of interest are recovered, which underwent a linear mixing. Asymptotic properties are studied of a classical unmixing estimator which is based on simultaneous diagonalization of the covariance matrix and an autocovariance matrix with lag τ. The main contributions are asymptotic results that can be applied to a large class of processes. In related literature, the processes are typically assumed to have weak correlations. This class is extended, and the unmixing estimator is considered under stronger dependency structures. In particular, the asymptotic behavior of the unmixing estimator is estimated for both long- and short-range dependent complex-valued processes. Consequently, this theory covers unmixing estimators that converge slower than the usual $\sqrt{T}$ and unmixing estimators that produce non-Gaussian asymptotic distributions. The presented methodology is a powerful preprocessing tool and highly applicable in several fields of statistics.Niko LietzénLauri ViitasaariPauliina IlmonenVTeXarticleAsymptotic theoryblind source separationlong-range dependencymultivariate analysisnoncentral limit theoremsApplied mathematics. Quantitative methodsT57-57.97MathematicsQA1-939ENModern Stochastics: Theory and Applications, Vol 8, Iss 4, Pp 475-508 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Asymptotic theory blind source separation long-range dependency multivariate analysis noncentral limit theorems Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
spellingShingle	Asymptotic theory blind source separation long-range dependency multivariate analysis noncentral limit theorems Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939 Niko Lietzén Lauri Viitasaari Pauliina Ilmonen Modeling temporally uncorrelated components of complex-valued stationary processes
description	A complex-valued linear mixture model is considered for discrete weakly stationary processes. Latent components of interest are recovered, which underwent a linear mixing. Asymptotic properties are studied of a classical unmixing estimator which is based on simultaneous diagonalization of the covariance matrix and an autocovariance matrix with lag τ. The main contributions are asymptotic results that can be applied to a large class of processes. In related literature, the processes are typically assumed to have weak correlations. This class is extended, and the unmixing estimator is considered under stronger dependency structures. In particular, the asymptotic behavior of the unmixing estimator is estimated for both long- and short-range dependent complex-valued processes. Consequently, this theory covers unmixing estimators that converge slower than the usual $\sqrt{T}$ and unmixing estimators that produce non-Gaussian asymptotic distributions. The presented methodology is a powerful preprocessing tool and highly applicable in several fields of statistics.
format	article
author	Niko Lietzén Lauri Viitasaari Pauliina Ilmonen
author_facet	Niko Lietzén Lauri Viitasaari Pauliina Ilmonen
author_sort	Niko Lietzén
title	Modeling temporally uncorrelated components of complex-valued stationary processes
title_short	Modeling temporally uncorrelated components of complex-valued stationary processes
title_full	Modeling temporally uncorrelated components of complex-valued stationary processes
title_fullStr	Modeling temporally uncorrelated components of complex-valued stationary processes
title_full_unstemmed	Modeling temporally uncorrelated components of complex-valued stationary processes
title_sort	modeling temporally uncorrelated components of complex-valued stationary processes
publisher	VTeX
publishDate	2021
url	https://doaj.org/article/b0865ce34d7c4be28e5a840251abab9b
work_keys_str_mv	AT nikolietzen modelingtemporallyuncorrelatedcomponentsofcomplexvaluedstationaryprocesses AT lauriviitasaari modelingtemporallyuncorrelatedcomponentsofcomplexvaluedstationaryprocesses AT pauliinailmonen modelingtemporallyuncorrelatedcomponentsofcomplexvaluedstationaryprocesses
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Modeling temporally uncorrelated components of complex-valued stationary processes

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