Stability of principal components under normal and non-normal parent populations and different covariance structures scenarios

Detalhes bibliográficos
Autor(a) principal: Bispo, Regina
Data de Publicação: 2023
Outros Autores: Marques, Filipe
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/162154
Resumo: Funding Information: This work is funded by national funds through the FCT–Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). The authors are grateful for the helpful suggestions made by a referee in an initial version of this manuscript. Publisher Copyright: © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
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spelling Stability of principal components under normal and non-normal parent populations and different covariance structures scenariosPrincipal componentseigenvectorsnonnormalitysimulationstabilityStatistics and ProbabilityModelling and SimulationStatistics, Probability and UncertaintyApplied MathematicsFunding Information: This work is funded by national funds through the FCT–Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). The authors are grateful for the helpful suggestions made by a referee in an initial version of this manuscript. Publisher Copyright: © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.Principal Component Analysis (PCA) is one of the most used multivariate techniques for dimension reduction assuming nowadays a particular relevance due to the increasingly common large datasets. Being mainly used as a descriptive/exploratory tool it does not require any explicit a priori assumption. However, regardless the parent population miss/unknown characterization, sample principal components are often used to characterize the parent population structure, as these are frequently targeted to visualize multivariate datasets on a 2D graphical display or to infer the first two latent dimensions. In this context, although the main goal might not be inferential, sample principal components may fail to provide a valid solution as principal components may vary considerably, depending on the extracted sample. The stability of the PCA solution is here studied considering normal and non-normal parent populations and three covariance structures scenarios. In addition, the effects of the covariance parameter, the dimension and the size of the sample are also investigated via Monte Carlo simulations. This study aims to understand how stability varies with the population and sample features, characterize the conditions under which PCA results are expected to be stable, and study a sample criterion for PCA stability.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNBispo, ReginaMarques, Filipe2024-01-11T22:26:12Z20232023-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article18application/pdfhttp://hdl.handle.net/10362/162154eng0094-9655PURE: 47288330https://doi.org/10.1080/00949655.2022.2125971info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T05:44:57Zoai:run.unl.pt:10362/162154Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:58:46.640967Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Stability of principal components under normal and non-normal parent populations and different covariance structures scenarios
title Stability of principal components under normal and non-normal parent populations and different covariance structures scenarios
spellingShingle Stability of principal components under normal and non-normal parent populations and different covariance structures scenarios
Bispo, Regina
Principal components
eigenvectors
nonnormality
simulation
stability
Statistics and Probability
Modelling and Simulation
Statistics, Probability and Uncertainty
Applied Mathematics
title_short Stability of principal components under normal and non-normal parent populations and different covariance structures scenarios
title_full Stability of principal components under normal and non-normal parent populations and different covariance structures scenarios
title_fullStr Stability of principal components under normal and non-normal parent populations and different covariance structures scenarios
title_full_unstemmed Stability of principal components under normal and non-normal parent populations and different covariance structures scenarios
title_sort Stability of principal components under normal and non-normal parent populations and different covariance structures scenarios
author Bispo, Regina
author_facet Bispo, Regina
Marques, Filipe
author_role author
author2 Marques, Filipe
author2_role author
dc.contributor.none.fl_str_mv DM - Departamento de Matemática
CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Bispo, Regina
Marques, Filipe
dc.subject.por.fl_str_mv Principal components
eigenvectors
nonnormality
simulation
stability
Statistics and Probability
Modelling and Simulation
Statistics, Probability and Uncertainty
Applied Mathematics
topic Principal components
eigenvectors
nonnormality
simulation
stability
Statistics and Probability
Modelling and Simulation
Statistics, Probability and Uncertainty
Applied Mathematics
description Funding Information: This work is funded by national funds through the FCT–Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). The authors are grateful for the helpful suggestions made by a referee in an initial version of this manuscript. Publisher Copyright: © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-01-01T00:00:00Z
2024-01-11T22:26:12Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/162154
url http://hdl.handle.net/10362/162154
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0094-9655
PURE: 47288330
https://doi.org/10.1080/00949655.2022.2125971
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 18
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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