Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation
Ano de defesa: | 2015 |
---|---|
Autor(a) principal: | |
Orientador(a): | |
Banca de defesa: | |
Tipo de documento: | Tese |
Tipo de acesso: | Acesso aberto |
Idioma: | eng |
Instituição de defesa: |
Universidade Federal de São Carlos
Câmpus São Carlos |
Programa de Pós-Graduação: |
Programa de Pós-Graduação em Estatística - PPGEs
|
Departamento: |
Não Informado pela instituição
|
País: |
Não Informado pela instituição
|
Palavras-chave em Português: | |
Área do conhecimento CNPq: | |
Link de acesso: | https://repositorio.ufscar.br/handle/ufscar/7226 |
Resumo: | In this thesis, we extend the analysis of multivariate Seemingly Unrelated Regression (SUR) Tobit models by modeling their nonlinear dependence structures through copulas. The capability in coupling together the diferent - and possibly non-normal - marginal distributions allows the exible modeling for the SUR Tobit models. In addition, the ability to capture the tail dependence of the SUR Tobit models where some data are censored (e.g., in econometric analysis, clinical essays, wide range of political and social phenomena, among others, data are commonly left-censored at zero point, or right-censored at a point d > 0) is another useful feature of copulas. Our study proposes a modified version of the (classical) Inference Function for Margins (IFM) method by Joe & Xu (1996), which we refer to as MIFM method, to obtain the (point) estimates of the marginal and copula association parameters. More specifically, we use a (frequentist) data augmentation technique at the second stage of the IFM method (the first stage of the MIFM method is equivalent to the first stage of the IFM method) to generate the censored observations and then estimate the copula parameter. This procedure (data augmentation and copula parameter estimation) is repeated until convergence. Such modification at the second stage of the usual method is justified in order to obtain continuous marginal distributions, which ensures the uniqueness of the resulting copula, as stated by Sklar (1959)'s theorem; and also to provide an unbiased estimate of the copula association parameter (the IFM method provides a biased estimate of the copula parameter in the presence of censored observations in the margins). Since the usual asymptotic approach, that is the computation of the asymptotic covariance matrix of the parameter estimates, is troublesome in this case, we also propose the use of resampling procedures (bootstrap methods, like standard normal and percentile by Efron & Tibshirani (1993), and basic bootstrap by Davison & Hinkley (1997)) to obtain con_dence intervals for the copula-based SUR Tobit model parameters. |
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Silva, Paulo Henrique Ferreira daLouzada Neto, Franciscohttp://lattes.cnpq.br/85385245970346432016-09-16T19:48:28Z2016-09-16T19:48:28Z2015-09-30SILVA, Paulo Henrique Ferreira da. Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation. 2015. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2015. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7226.https://repositorio.ufscar.br/handle/ufscar/7226In this thesis, we extend the analysis of multivariate Seemingly Unrelated Regression (SUR) Tobit models by modeling their nonlinear dependence structures through copulas. The capability in coupling together the diferent - and possibly non-normal - marginal distributions allows the exible modeling for the SUR Tobit models. In addition, the ability to capture the tail dependence of the SUR Tobit models where some data are censored (e.g., in econometric analysis, clinical essays, wide range of political and social phenomena, among others, data are commonly left-censored at zero point, or right-censored at a point d > 0) is another useful feature of copulas. Our study proposes a modified version of the (classical) Inference Function for Margins (IFM) method by Joe & Xu (1996), which we refer to as MIFM method, to obtain the (point) estimates of the marginal and copula association parameters. More specifically, we use a (frequentist) data augmentation technique at the second stage of the IFM method (the first stage of the MIFM method is equivalent to the first stage of the IFM method) to generate the censored observations and then estimate the copula parameter. This procedure (data augmentation and copula parameter estimation) is repeated until convergence. Such modification at the second stage of the usual method is justified in order to obtain continuous marginal distributions, which ensures the uniqueness of the resulting copula, as stated by Sklar (1959)'s theorem; and also to provide an unbiased estimate of the copula association parameter (the IFM method provides a biased estimate of the copula parameter in the presence of censored observations in the margins). Since the usual asymptotic approach, that is the computation of the asymptotic covariance matrix of the parameter estimates, is troublesome in this case, we also propose the use of resampling procedures (bootstrap methods, like standard normal and percentile by Efron & Tibshirani (1993), and basic bootstrap by Davison & Hinkley (1997)) to obtain con_dence intervals for the copula-based SUR Tobit model parameters.Nesta tese de doutorado, consideramos os chamados modelos SUR (da expressão Seemingly Unrelated Regression) Tobit multivariados e estendemos a análise de tais modelos ao empregar funções de cópula para modelar estruturas com dependência não linear. As cópulas, dentre outras características, possuem a importante habilidade (vantagem) de capturar/modelar a dependência na(s) cauda(s) do modelo SUR Tobit em que alguns dados são censurados (por exemplo, em análise econométrica, ensaios clínicos e em ampla gama de fenômenos políticos e sociais, dentre outros, os dados são geralmente censurados à esquerda no ponto zero, ou à direita em um ponto d > 0 qualquer). Neste trabalho, propomos uma versão modificada do método clássico da Inferência para as Marginais (IFM, da expressão Inference Function for Margins), originalmente proposto por Joe & Xu (1996), a qual chamamos de MIFM, para estimação (pontual) dos parâmetros do modelo SUR Tobit multivariado baseado em cópula. Mais especificamente, empregamos uma técnica (frequentista) de ampliação de dados no segundo estágio do método IFM (o primeiro estágio do método MIFM é igual ao primeiro estágio do método IFM) para gerar as observações censuradas e, então, estimamos o parâmetro de dependência da cópula. Repetimos tal procedimento (ampliação de dados e estimação do parâmetro da cópula) até obter convergência. As razões para esta modificação no segundo estágio do método usual, são as seguintes: primeiro, construir/obter distribuições marginais contínuas, atendendo, então, ao teorema de unicidade da cópula resultante de Sklar (Sklar, 1959); e segundo, fornecer uma estimativa não viesada para o parâmetro da cópula (uma vez que o método IFM produz estimativas viesadas do parâmetro da cópula na presença de observações censuradas nas marginais). Tendo em vista a dificuldade adicional em calcular/obter a matriz de covariâncias assintótica das estimativas dos parâmetros, também propomos o uso de procedimentos de reamostragem (métodos bootstrap, tais como normal padrão e percentil, propostos por Efron & Tibshirani (1993), e básico, proposto por Davison & Hinkley (1997)) para a construção de intervalos de confiança para os parâmetros do modelo SUR Tobit baseado em cópula.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)engUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Estatística - PPGEsUFSCarProbabilidadesIntervalos de confiançaBootstrap (Estatística)CópulaAmpliação de dadosMétodo de inferência para marginais modificadoCIENCIAS EXATAS E DA TERRACIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAOMultivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisOnlineinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTesePHFS.pdfTesePHFS.pdfapplication/pdf1284969https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7226/1/TesePHFS.pdf4ebcbf7e8a84023d87dab3c54c19f103MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7226/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTTesePHFS.pdf.txtTesePHFS.pdf.txtExtracted texttext/plain325787https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7226/3/TesePHFS.pdf.txt93cf57392bd6d057c622057b9bdd159fMD53THUMBNAILTesePHFS.pdf.jpgTesePHFS.pdf.jpgIM Thumbnailimage/jpeg6197https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/7226/4/TesePHFS.pdf.jpgba9f7881ea0702b0fdb2e8260868c96aMD54ufscar/72262019-09-11 02:53:03.052oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-05-25T12:52:12.704461Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.eng.fl_str_mv |
Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation |
title |
Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation |
spellingShingle |
Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation Silva, Paulo Henrique Ferreira da Probabilidades Intervalos de confiança Bootstrap (Estatística) Cópula Ampliação de dados Método de inferência para marginais modificado CIENCIAS EXATAS E DA TERRA CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
title_short |
Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation |
title_full |
Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation |
title_fullStr |
Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation |
title_full_unstemmed |
Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation |
title_sort |
Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation |
author |
Silva, Paulo Henrique Ferreira da |
author_facet |
Silva, Paulo Henrique Ferreira da |
author_role |
author |
dc.contributor.advisor1Lattes.none.fl_str_mv |
|
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/8538524597034643 |
dc.contributor.author.fl_str_mv |
Silva, Paulo Henrique Ferreira da |
dc.contributor.advisor1.fl_str_mv |
Louzada Neto, Francisco |
contributor_str_mv |
Louzada Neto, Francisco |
dc.subject.por.fl_str_mv |
Probabilidades Intervalos de confiança Bootstrap (Estatística) Cópula Ampliação de dados Método de inferência para marginais modificado |
topic |
Probabilidades Intervalos de confiança Bootstrap (Estatística) Cópula Ampliação de dados Método de inferência para marginais modificado CIENCIAS EXATAS E DA TERRA CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
description |
In this thesis, we extend the analysis of multivariate Seemingly Unrelated Regression (SUR) Tobit models by modeling their nonlinear dependence structures through copulas. The capability in coupling together the diferent - and possibly non-normal - marginal distributions allows the exible modeling for the SUR Tobit models. In addition, the ability to capture the tail dependence of the SUR Tobit models where some data are censored (e.g., in econometric analysis, clinical essays, wide range of political and social phenomena, among others, data are commonly left-censored at zero point, or right-censored at a point d > 0) is another useful feature of copulas. Our study proposes a modified version of the (classical) Inference Function for Margins (IFM) method by Joe & Xu (1996), which we refer to as MIFM method, to obtain the (point) estimates of the marginal and copula association parameters. More specifically, we use a (frequentist) data augmentation technique at the second stage of the IFM method (the first stage of the MIFM method is equivalent to the first stage of the IFM method) to generate the censored observations and then estimate the copula parameter. This procedure (data augmentation and copula parameter estimation) is repeated until convergence. Such modification at the second stage of the usual method is justified in order to obtain continuous marginal distributions, which ensures the uniqueness of the resulting copula, as stated by Sklar (1959)'s theorem; and also to provide an unbiased estimate of the copula association parameter (the IFM method provides a biased estimate of the copula parameter in the presence of censored observations in the margins). Since the usual asymptotic approach, that is the computation of the asymptotic covariance matrix of the parameter estimates, is troublesome in this case, we also propose the use of resampling procedures (bootstrap methods, like standard normal and percentile by Efron & Tibshirani (1993), and basic bootstrap by Davison & Hinkley (1997)) to obtain con_dence intervals for the copula-based SUR Tobit model parameters. |
publishDate |
2015 |
dc.date.issued.fl_str_mv |
2015-09-30 |
dc.date.accessioned.fl_str_mv |
2016-09-16T19:48:28Z |
dc.date.available.fl_str_mv |
2016-09-16T19:48:28Z |
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 |
SILVA, Paulo Henrique Ferreira da. Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation. 2015. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2015. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7226. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/7226 |
identifier_str_mv |
SILVA, Paulo Henrique Ferreira da. Multivariate Copula-based SUR Tobit Models : a modified inference function for margins and interval estimation. 2015. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2015. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7226. |
url |
https://repositorio.ufscar.br/handle/ufscar/7226 |
dc.language.iso.fl_str_mv |
eng |
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eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Estatística - PPGEs |
dc.publisher.initials.fl_str_mv |
UFSCar |
publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.source.none.fl_str_mv |
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