The 123 theorem of Probability Theory and Copositive Matrices

Detalhes bibliográficos
Autor(a) principal: Kovacec, Alexander
Data de Publicação: 2014
Outros Autores: Moreira, Miguel M. R., Martins, David P.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/102687
https://doi.org/10.2478/spma-2014-0016
Resumo: Alon and Yuster give for independent identically distributed real or vector valued random variables X, Y combinatorially proved estimates of the form Prob(‖X − Y‖ b) c Prob(‖X − Y‖ a). We derive these using copositive matrices instead. By the same method we also give estimates for the real valued case, involving X + Y and X − Y, due to Siegmund-Schultze and von Weizsäcker as generalized by Dong, Li and Li. Furthermore, we formulate a version of the above inequalities as an integral inequality for monotone functions.
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spelling The 123 theorem of Probability Theory and Copositive Matricesprobabilistic inequalitiescopositivityintegral inequalityAlon and Yuster give for independent identically distributed real or vector valued random variables X, Y combinatorially proved estimates of the form Prob(‖X − Y‖ b) c Prob(‖X − Y‖ a). We derive these using copositive matrices instead. By the same method we also give estimates for the real valued case, involving X + Y and X − Y, due to Siegmund-Schultze and von Weizsäcker as generalized by Dong, Li and Li. Furthermore, we formulate a version of the above inequalities as an integral inequality for monotone functions.2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/102687http://hdl.handle.net/10316/102687https://doi.org/10.2478/spma-2014-0016eng2300-7451Kovacec, AlexanderMoreira, Miguel M. R.Martins, David P.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:RCAAP2022-10-06T20:31:41Zoai:estudogeral.uc.pt:10316/102687Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:19:37.586881Repositório 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 The 123 theorem of Probability Theory and Copositive Matrices
title The 123 theorem of Probability Theory and Copositive Matrices
spellingShingle The 123 theorem of Probability Theory and Copositive Matrices
Kovacec, Alexander
probabilistic inequalities
copositivity
integral inequality
title_short The 123 theorem of Probability Theory and Copositive Matrices
title_full The 123 theorem of Probability Theory and Copositive Matrices
title_fullStr The 123 theorem of Probability Theory and Copositive Matrices
title_full_unstemmed The 123 theorem of Probability Theory and Copositive Matrices
title_sort The 123 theorem of Probability Theory and Copositive Matrices
author Kovacec, Alexander
author_facet Kovacec, Alexander
Moreira, Miguel M. R.
Martins, David P.
author_role author
author2 Moreira, Miguel M. R.
Martins, David P.
author2_role author
author
dc.contributor.author.fl_str_mv Kovacec, Alexander
Moreira, Miguel M. R.
Martins, David P.
dc.subject.por.fl_str_mv probabilistic inequalities
copositivity
integral inequality
topic probabilistic inequalities
copositivity
integral inequality
description Alon and Yuster give for independent identically distributed real or vector valued random variables X, Y combinatorially proved estimates of the form Prob(‖X − Y‖ b) c Prob(‖X − Y‖ a). We derive these using copositive matrices instead. By the same method we also give estimates for the real valued case, involving X + Y and X − Y, due to Siegmund-Schultze and von Weizsäcker as generalized by Dong, Li and Li. Furthermore, we formulate a version of the above inequalities as an integral inequality for monotone functions.
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/10316/102687
http://hdl.handle.net/10316/102687
https://doi.org/10.2478/spma-2014-0016
url http://hdl.handle.net/10316/102687
https://doi.org/10.2478/spma-2014-0016
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2300-7451
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
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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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