A Note on Weighted Sums of Associated Random Variables

Detalhes bibliográficos
Autor(a) principal: Çağin, T.
Data de Publicação: 2014
Outros Autores: Oliveira, P. E.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/43682
https://doi.org/10.1007/s10474-014-0397-1
Resumo: We prove the convergence of weighted sums of associated random variables normalized by $n^{1/p}$, $p\in(1,2)$, assuming the existence of moments somewhat larger than $p$, depending on the behaviour of the weights, improving on previous results by getting closer to the moment assumption used for the case of constant weights. Besides moment conditions we assume a convenient behaviour either on truncated covariances or on joint tail probabilities. Our results extend analogous characterizations known for sums of independent or negatively dependent random variables.
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spelling A Note on Weighted Sums of Associated Random Variablesweighted sumsassociated random variablesalmost sure convergenceMarcinkiewicz-Zygmund strong law of large numbersWe prove the convergence of weighted sums of associated random variables normalized by $n^{1/p}$, $p\in(1,2)$, assuming the existence of moments somewhat larger than $p$, depending on the behaviour of the weights, improving on previous results by getting closer to the moment assumption used for the case of constant weights. Besides moment conditions we assume a convenient behaviour either on truncated covariances or on joint tail probabilities. Our results extend analogous characterizations known for sums of independent or negatively dependent random variables.Springer2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43682http://hdl.handle.net/10316/43682https://doi.org/10.1007/s10474-014-0397-1https://doi.org/10.1007/s10474-014-0397-1enghttps://link.springer.com/article/10.1007/s10474-014-0397-1Çağin, T.Oliveira, P. E.info: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:RCAAP2021-06-29T10:02:52Zoai:estudogeral.uc.pt:10316/43682Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:26.501289Repositório 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 A Note on Weighted Sums of Associated Random Variables
title A Note on Weighted Sums of Associated Random Variables
spellingShingle A Note on Weighted Sums of Associated Random Variables
Çağin, T.
weighted sums
associated random variables
almost sure convergence
Marcinkiewicz-Zygmund strong law of large numbers
title_short A Note on Weighted Sums of Associated Random Variables
title_full A Note on Weighted Sums of Associated Random Variables
title_fullStr A Note on Weighted Sums of Associated Random Variables
title_full_unstemmed A Note on Weighted Sums of Associated Random Variables
title_sort A Note on Weighted Sums of Associated Random Variables
author Çağin, T.
author_facet Çağin, T.
Oliveira, P. E.
author_role author
author2 Oliveira, P. E.
author2_role author
dc.contributor.author.fl_str_mv Çağin, T.
Oliveira, P. E.
dc.subject.por.fl_str_mv weighted sums
associated random variables
almost sure convergence
Marcinkiewicz-Zygmund strong law of large numbers
topic weighted sums
associated random variables
almost sure convergence
Marcinkiewicz-Zygmund strong law of large numbers
description We prove the convergence of weighted sums of associated random variables normalized by $n^{1/p}$, $p\in(1,2)$, assuming the existence of moments somewhat larger than $p$, depending on the behaviour of the weights, improving on previous results by getting closer to the moment assumption used for the case of constant weights. Besides moment conditions we assume a convenient behaviour either on truncated covariances or on joint tail probabilities. Our results extend analogous characterizations known for sums of independent or negatively dependent random variables.
publishDate 2014
dc.date.none.fl_str_mv 2014
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/10316/43682
http://hdl.handle.net/10316/43682
https://doi.org/10.1007/s10474-014-0397-1
https://doi.org/10.1007/s10474-014-0397-1
url http://hdl.handle.net/10316/43682
https://doi.org/10.1007/s10474-014-0397-1
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://link.springer.com/article/10.1007/s10474-014-0397-1
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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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