Consistency of Decision in Finite and Numerable Multinomial Models

Detalhes bibliográficos
Autor(a) principal: Akoto, Isaac
Data de Publicação: 2023
Outros Autores: Mexia, João T.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/155255
Resumo: Publisher Copyright: © 2023 by the authors. This research received no external funding.
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spelling Consistency of Decision in Finite and Numerable Multinomial Modelsdecision theoryestimatorsstochastic convergenceComputer Science (miscellaneous)Mathematics(all)Engineering (miscellaneous)Publisher Copyright: © 2023 by the authors. This research received no external funding.The multinomial distribution is often used in modeling categorical data because it describes the probability of a random observation being assigned to one of several mutually exclusive categories. Given a finite or numerable multinomial model (Formula presented.) whose decision is indexed by a parameter (Formula presented.) and having a cost (Formula presented.) depending on (Formula presented.) and on (Formula presented.), we show that, under general conditions, the probability of taking the least cost decision tends to 1 when n tends to ∞, i.e., we showed that the cost decision is consistent, representing a Statistical Decision Theory approach to the concept of consistency, which is not much considered in the literature. Thus, under these conditions, we have consistency in the decision making. The key result is that the estimator (Formula presented.) with components (Formula presented.), where (Formula presented.) is the number of times we obtain the ith result when we have a sample of size n, is a consistent estimator of (Formula presented.). This result holds both for finite and numerable models. By this result, we were able to incorporate a more general form for consistency for the cost function of a multinomial model.CMA - Centro de Matemática e AplicaçõesRUNAkoto, IsaacMexia, João T.2023-07-13T22:19:16Z2023-05-242023-05-24T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article8application/pdfhttp://hdl.handle.net/10362/155255engAkoto, I., & Mexia, J. T. (2023). Consistency of Decision in Finite and Numerable Multinomial Models. Mathematics, 11(11), [2434]. https://doi.org/10.3390/math111124342227-7390PURE: 66169593https://doi.org/10.3390/math11112434info: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:RCAAP2024-03-11T05:37:48Zoai:run.unl.pt:10362/155255Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:56:00.043037Repositório 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 Consistency of Decision in Finite and Numerable Multinomial Models
title Consistency of Decision in Finite and Numerable Multinomial Models
spellingShingle Consistency of Decision in Finite and Numerable Multinomial Models
Akoto, Isaac
decision theory
estimators
stochastic convergence
Computer Science (miscellaneous)
Mathematics(all)
Engineering (miscellaneous)
title_short Consistency of Decision in Finite and Numerable Multinomial Models
title_full Consistency of Decision in Finite and Numerable Multinomial Models
title_fullStr Consistency of Decision in Finite and Numerable Multinomial Models
title_full_unstemmed Consistency of Decision in Finite and Numerable Multinomial Models
title_sort Consistency of Decision in Finite and Numerable Multinomial Models
author Akoto, Isaac
author_facet Akoto, Isaac
Mexia, João T.
author_role author
author2 Mexia, João T.
author2_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Akoto, Isaac
Mexia, João T.
dc.subject.por.fl_str_mv decision theory
estimators
stochastic convergence
Computer Science (miscellaneous)
Mathematics(all)
Engineering (miscellaneous)
topic decision theory
estimators
stochastic convergence
Computer Science (miscellaneous)
Mathematics(all)
Engineering (miscellaneous)
description Publisher Copyright: © 2023 by the authors. This research received no external funding.
publishDate 2023
dc.date.none.fl_str_mv 2023-07-13T22:19:16Z
2023-05-24
2023-05-24T00:00:00Z
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/10362/155255
url http://hdl.handle.net/10362/155255
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Akoto, I., & Mexia, J. T. (2023). Consistency of Decision in Finite and Numerable Multinomial Models. Mathematics, 11(11), [2434]. https://doi.org/10.3390/math11112434
2227-7390
PURE: 66169593
https://doi.org/10.3390/math11112434
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 8
application/pdf
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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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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