Modeling temporally uncorrelated components of complex-valued stationary processes

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorLietzén, Nikoen_US
dc.contributor.authorViitasaari, Laurien_US
dc.contributor.authorIlmonen, Pauliinaen_US
dc.contributor.departmentDepartment of Mathematics and Systems Analysisen
dc.contributor.groupauthorMathematical Statistics and Data Scienceen
dc.date.accessioned2021-12-08T07:30:30Z
dc.date.available2021-12-08T07:30:30Z
dc.date.issued2021-11en_US
dc.descriptionFunding Information: N. Lietzén gratefully acknowledges financial support from the Emil Aaltonen Foundation (Grant 180144 N) and from the Academy of Finland (Grant 321968). Funding Information: The authors would like to thank Katariina Kilpinen for providing the photographs to Section 5. The authors would like to thank the two anonymous referees for their insightful comments that helped to improve this paper greatly.N. Lietzen gratefully acknowledges financial support from the Emil Aaltonen Foundation (Grant 180144 N) and from the Academy of Finland (Grant 321968). Publisher Copyright: © 2021 The Author(s). Published by VTeX. Open access article under the CC BY license.
dc.description.abstractA 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√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.en
dc.description.versionPeer revieweden
dc.format.extent34
dc.format.extent475-508
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationLietzén, N, Viitasaari, L & Ilmonen, P 2021, ' Modeling temporally uncorrelated components of complex-valued stationary processes ', Modern Stochastics: Theory and Applications, vol. 8, no. 4, pp. 475-508 . https://doi.org/10.15559/21-VMSTA190en
dc.identifier.doi10.15559/21-VMSTA190en_US
dc.identifier.issn2351-6046
dc.identifier.otherPURE UUID: 059a5dc1-d105-4f33-b0d0-b8bbc79b583aen_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/059a5dc1-d105-4f33-b0d0-b8bbc79b583aen_US
dc.identifier.otherPURE LINK: http://www.scopus.com/inward/record.url?scp=85119671314&partnerID=8YFLogxKen_US
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/76421496/Modeling_temporally_uncorrelated_components_of_complex_valued_stationary_processes.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/111433
dc.identifier.urnURN:NBN:fi:aalto-2021120810577
dc.language.isoenen
dc.publisherVTeX
dc.relation.ispartofseriesModern Stochastics: Theory and Applicationsen
dc.relation.ispartofseriesVolume 8, issue 4en
dc.rightsopenAccessen
dc.subject.keywordAsymptotic theoryen_US
dc.subject.keywordBlind source separationen_US
dc.subject.keywordLong-range dependencyen_US
dc.subject.keywordMultivariate analysisen_US
dc.subject.keywordNoncentral limit theoremsen_US
dc.titleModeling temporally uncorrelated components of complex-valued stationary processesen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionpublishedVersion

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