ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/84943 |
Resumo: | We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of weakly dependent structures. We prove the Strong Law of Large Numbers with the characterization of convergence rates which is almost optimal, in the sense that it is arbitrarily close to the optimal rate for independent variables. Moreover, we prove an inequality comparing the joint distributions with the product distributions of the margins, similar to the well known Newman's inequality for characteristic functions of associated variables. As a consequence, we prove the Central Limit Theorem together with its functional counterpart, and also the convergence of the empirical process for this class of weak dependent variables. |
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7160 |
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ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLESCentral Limit TheoremConvergence rateL-weak dependenceStrong law of large numbersWe consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of weakly dependent structures. We prove the Strong Law of Large Numbers with the characterization of convergence rates which is almost optimal, in the sense that it is arbitrarily close to the optimal rate for independent variables. Moreover, we prove an inequality comparing the joint distributions with the product distributions of the margins, similar to the well known Newman's inequality for characteristic functions of associated variables. As a consequence, we prove the Central Limit Theorem together with its functional counterpart, and also the convergence of the empirical process for this class of weak dependent variables.2018info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/84943http://hdl.handle.net/10316/84943por0868-6904Arab, IdirOliveira, Pauloinfo: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:RCAAP2020-05-29T10:05:17Zoai:estudogeral.uc.pt:10316/84943Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:06:26.197889Repositório 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 |
ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES |
title |
ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES |
spellingShingle |
ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES Arab, Idir Central Limit Theorem Convergence rate L-weak dependence Strong law of large numbers |
title_short |
ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES |
title_full |
ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES |
title_fullStr |
ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES |
title_full_unstemmed |
ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES |
title_sort |
ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES |
author |
Arab, Idir |
author_facet |
Arab, Idir Oliveira, Paulo |
author_role |
author |
author2 |
Oliveira, Paulo |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Arab, Idir Oliveira, Paulo |
dc.subject.por.fl_str_mv |
Central Limit Theorem Convergence rate L-weak dependence Strong law of large numbers |
topic |
Central Limit Theorem Convergence rate L-weak dependence Strong law of large numbers |
description |
We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of weakly dependent structures. We prove the Strong Law of Large Numbers with the characterization of convergence rates which is almost optimal, in the sense that it is arbitrarily close to the optimal rate for independent variables. Moreover, we prove an inequality comparing the joint distributions with the product distributions of the margins, similar to the well known Newman's inequality for characteristic functions of associated variables. As a consequence, we prove the Central Limit Theorem together with its functional counterpart, and also the convergence of the empirical process for this class of weak dependent variables. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018 |
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/10316/84943 http://hdl.handle.net/10316/84943 |
url |
http://hdl.handle.net/10316/84943 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
0868-6904 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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 |
institution |
RCAAP |
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 |
repository.mail.fl_str_mv |
|
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1799133956488036352 |