Consistency of Decision in Finite and Numerable Multinomial Models
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | |
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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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 |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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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