New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/18687 |
Resumo: | In this dissertation, we propose families of linear and partially linear quantile regression models, where the response variable follows a reparameterized Marshall-Olkin distribution with support on the real line. This distribution presents great flexibility and arises from applying the Marshall- Olkin methodology to distributions of the location-scale family and then reparameterizing the location parameter as a function of the quantile. For this reason, the new distribution’s name is reparameterized Marshall-Olkin, which contains quantile, scale and skewness parameters. The first family has a structure similar to the generalized linear models that enable the use of the maximum likelihood method. Consequently, we calculate the expressions of the score vector and the observed information matrix to perform the statistical inference. The adequacy of models and outlier observations are studied through three types of residuals. In order to assess the sensitivity of the estimates, measures of global and local influence are developed. The second family is an extension of the first family by adding the description of the nonlinear relationship between the quantiles of the response variable and a continuous variable through B-splines. In this family, statistical inference tools are based on the penalized log-likelihood function. Also, analogously to the first family, the residuals and measures of global and local influence are presented. Two examples of applications are considered that illustrate the usefulness of the proposed families for data sets in the areas of health and nutrition. |
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Cortés, IsaacAndrade, Mário de Castrohttp://lattes.cnpq.br/6518161034709249http://lattes.cnpq.br/5497894016400216cbd00e62-b2af-499a-926f-f588df2edc4d2023-10-02T14:31:28Z2023-10-02T14:31:28Z2023-07-31CORTÉS, Isaac. New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions. 2023. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2023. Disponível em: https://repositorio.ufscar.br/handle/ufscar/18687.https://repositorio.ufscar.br/handle/ufscar/18687In this dissertation, we propose families of linear and partially linear quantile regression models, where the response variable follows a reparameterized Marshall-Olkin distribution with support on the real line. This distribution presents great flexibility and arises from applying the Marshall- Olkin methodology to distributions of the location-scale family and then reparameterizing the location parameter as a function of the quantile. For this reason, the new distribution’s name is reparameterized Marshall-Olkin, which contains quantile, scale and skewness parameters. The first family has a structure similar to the generalized linear models that enable the use of the maximum likelihood method. Consequently, we calculate the expressions of the score vector and the observed information matrix to perform the statistical inference. The adequacy of models and outlier observations are studied through three types of residuals. In order to assess the sensitivity of the estimates, measures of global and local influence are developed. The second family is an extension of the first family by adding the description of the nonlinear relationship between the quantiles of the response variable and a continuous variable through B-splines. In this family, statistical inference tools are based on the penalized log-likelihood function. Also, analogously to the first family, the residuals and measures of global and local influence are presented. Two examples of applications are considered that illustrate the usefulness of the proposed families for data sets in the areas of health and nutrition.Nesta tese, propomos famílias de modelos de regressão quantílica linear e parcialmente linear, onde a variável resposta segue uma distribuição Marshall-Olkin reparametrizada com suporte na reta real. Esta distribuição apresenta uma grande flexibilidade que surge ao aplicar a metodologia Marshall-Olkin as distribuições da família de locação-escala, logo reparametrizando o parâmetro de locação em função do quantil. Por esse motivo, o nome da nova distribuição é Marshall-Olkin reparametrizada, que contém parâmetros de quantil, escala e assimetria. A primeira família tem uma estrutura semelhante aos modelos lineares generalizados, que permite a utilização do método da máxima verossimilhança. Consequentemente, calculamos as expressões do vetor escore e da matriz de informação observada para realizar a inferência estatística. A adequação dos modelos e observações discrepantes são estudadas por meio de três tipos de resíduos. Para avaliar a sensibilidade das estimativas são desenvolvidas medidas de influência global e local. A segunda família é uma extensão da primeira família por adicionar a descrição da relação não linear entre os quantis da variável resposta e uma variável contínua por meio de B-splines. Nesta família as ferramentas de inferência estatística são baseadas na função de log-verossimilhança penalizada. Também, analogamente à primeira família são apresentados os resíduos e as medidas de influência global e local. São considerados dois exemplos de aplicações que ilustram a utilidade das famílias propostas para conjuntos de dados na área de saúde e nutrição.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)CAPES: Código de financiamento 001engUniversidade Federal de São CarlosCâmpus São CarlosPrograma Interinstitucional de Pós-Graduação em Estatística - PIPGEsUFSCarAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessRegressão quantílicaEstimadores de máxima verossimilhançaInfluência globalInfluência localAnálise residualEstimadores de máxima verossimilhança penalizadaP-splinesQuantile regressionMaximum likelihood estimatorsGlobal influenceLocal influenceResidual analysisPenalized maximum likelihood estimatorsCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAONew families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributionsNovas famílias de modelos de regressão quantílica linear e parcialmente linear sob distribuições Marshall-Olkin reparametrizadasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis6006009080f8a3-6648-46f5-86f8-492a34caf1d6reponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTese_Isaac_Ufscar.pdfTese_Isaac_Ufscar.pdfTese Isaac Cortés Olmosapplication/pdf16314971https://repositorio.ufscar.br/bitstream/ufscar/18687/1/Tese_Isaac_Ufscar.pdfc9dff52887c17991b459365a4cca2f00MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8810https://repositorio.ufscar.br/bitstream/ufscar/18687/2/license_rdff337d95da1fce0a22c77480e5e9a7aecMD52TEXTTese_Isaac_Ufscar.pdf.txtTese_Isaac_Ufscar.pdf.txtExtracted texttext/plain196952https://repositorio.ufscar.br/bitstream/ufscar/18687/3/Tese_Isaac_Ufscar.pdf.txtc144f69bc011d6fb0a9138c0bbcf03a0MD53ufscar/186872024-05-14 17:16:15.434oai:repositorio.ufscar.br:ufscar/18687Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222024-05-14T17:16:15Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.eng.fl_str_mv |
New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions |
dc.title.alternative.por.fl_str_mv |
Novas famílias de modelos de regressão quantílica linear e parcialmente linear sob distribuições Marshall-Olkin reparametrizadas |
title |
New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions |
spellingShingle |
New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions Cortés, Isaac Regressão quantílica Estimadores de máxima verossimilhança Influência global Influência local Análise residual Estimadores de máxima verossimilhança penalizada P-splines Quantile regression Maximum likelihood estimators Global influence Local influence Residual analysis Penalized maximum likelihood estimators CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
title_short |
New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions |
title_full |
New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions |
title_fullStr |
New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions |
title_full_unstemmed |
New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions |
title_sort |
New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions |
author |
Cortés, Isaac |
author_facet |
Cortés, Isaac |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/5497894016400216 |
dc.contributor.author.fl_str_mv |
Cortés, Isaac |
dc.contributor.advisor1.fl_str_mv |
Andrade, Mário de Castro |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/6518161034709249 |
dc.contributor.authorID.fl_str_mv |
cbd00e62-b2af-499a-926f-f588df2edc4d |
contributor_str_mv |
Andrade, Mário de Castro |
dc.subject.por.fl_str_mv |
Regressão quantílica Estimadores de máxima verossimilhança Influência global Influência local Análise residual Estimadores de máxima verossimilhança penalizada |
topic |
Regressão quantílica Estimadores de máxima verossimilhança Influência global Influência local Análise residual Estimadores de máxima verossimilhança penalizada P-splines Quantile regression Maximum likelihood estimators Global influence Local influence Residual analysis Penalized maximum likelihood estimators CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
dc.subject.eng.fl_str_mv |
P-splines Quantile regression Maximum likelihood estimators Global influence Local influence Residual analysis Penalized maximum likelihood estimators |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
description |
In this dissertation, we propose families of linear and partially linear quantile regression models, where the response variable follows a reparameterized Marshall-Olkin distribution with support on the real line. This distribution presents great flexibility and arises from applying the Marshall- Olkin methodology to distributions of the location-scale family and then reparameterizing the location parameter as a function of the quantile. For this reason, the new distribution’s name is reparameterized Marshall-Olkin, which contains quantile, scale and skewness parameters. The first family has a structure similar to the generalized linear models that enable the use of the maximum likelihood method. Consequently, we calculate the expressions of the score vector and the observed information matrix to perform the statistical inference. The adequacy of models and outlier observations are studied through three types of residuals. In order to assess the sensitivity of the estimates, measures of global and local influence are developed. The second family is an extension of the first family by adding the description of the nonlinear relationship between the quantiles of the response variable and a continuous variable through B-splines. In this family, statistical inference tools are based on the penalized log-likelihood function. Also, analogously to the first family, the residuals and measures of global and local influence are presented. Two examples of applications are considered that illustrate the usefulness of the proposed families for data sets in the areas of health and nutrition. |
publishDate |
2023 |
dc.date.accessioned.fl_str_mv |
2023-10-02T14:31:28Z |
dc.date.available.fl_str_mv |
2023-10-02T14:31:28Z |
dc.date.issued.fl_str_mv |
2023-07-31 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
CORTÉS, Isaac. New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions. 2023. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2023. Disponível em: https://repositorio.ufscar.br/handle/ufscar/18687. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/18687 |
identifier_str_mv |
CORTÉS, Isaac. New families of linear and partially linear quantile regression models under reparameterized Marshall-Olkin distributions. 2023. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2023. Disponível em: https://repositorio.ufscar.br/handle/ufscar/18687. |
url |
https://repositorio.ufscar.br/handle/ufscar/18687 |
dc.language.iso.fl_str_mv |
eng |
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eng |
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600 600 |
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9080f8a3-6648-46f5-86f8-492a34caf1d6 |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
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Universidade Federal de São Carlos Câmpus São Carlos |
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Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs |
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UFSCar |
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Universidade Federal de São Carlos Câmpus São Carlos |
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