Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape
Ano de defesa: | 2021 |
---|---|
Autor(a) principal: | |
Orientador(a): | |
Banca de defesa: | |
Tipo de documento: | Tese |
Tipo de acesso: | Acesso embargado |
Idioma: | eng |
Instituição de defesa: |
Universidade Federal de Pernambuco
|
Programa de Pós-Graduação: |
Programa de Pos Graduacao em Estatistica
|
Departamento: |
Não Informado pela instituição
|
País: |
Brasil
|
Palavras-chave em Português: | |
Link de acesso: | https://repositorio.ufpe.br/handle/123456789/41385 |
Resumo: | This thesis presents two independent themes with different background. The first theme presents a new method for detecting spatial clusters, that is, a method for detecting regions with a high concentration of spatial phenomena, compared to a expected number, given a random distribution of events. The main contribution is to present a nonparametric method based on empirical likelihood functions, as an alternative to traditional methods of using clusters (scan). In this way, no distribution family is required for the variable of interest. To evaluate the method, simulation studies were carried out considering the zero-inflated poisson model, comparing the results with the scan method proposed by Kuldorff. The results show that the new method reduces the error probabilities of the type I for zero inflated, with low power for cluster with less than 8 locations. A study was carried out for Measles data in São Paulo, Brazil, which present a excess of zeros. Only the Kulldorff scanning method identified the existence of a cluster, located and centered on the capital São Paulo. However, if a cluster is identified by the Kulldorff method in the presence of inflated and when not confirmed by the non-parametric approach, it is recommended that interpretations be performed with caution due to a high probability type error associated with Kulldorff method when model is not well specified. The second theme aims to present two new approaches to robust estimation for generalized additive models of location, scale and shape - GAMLSS, which focus on contamination situations in the tails of distributions. The main motivation is the scarcity of robust methods for GAMLSS models. The thesis were subdivided into two topics. The first topic presents a proposal that seeks transformations in order to limit the influence function associated with the probability distribution of interest, modifying the logarithm structure of the likelihood function, using concepts of censorship. It also features: the robust GAMLSS method proposed by Rigby et al. (2019), considering the gamma distribution, presenting the bias corrections for the estimators; a modification of the method proposed by Rigby et al. (2019), considering the weight of observations in the estimation; and, finally, a large simulation study to evaluate the proposals, using the gamma distribution and contamination in the right tail of the distribution. The second topic is based on a simple adaptive truncation, where observations identified as possible outliers are verified and, if necessary, removed by truncation of the response variable distribution. The simulation studies used the gamma and beta distributions, left and right tail contamination, and three distinct models: parametric models with and without covariates and non-parametric models. The results show that, compared to existing methods in the literature, the truncated adaptive method has a better performance with lower mean square error and lower variability in most simulated scenarios. The overall performances of the proposals are illustrated through three applications: brain image resonance data, using bivariate smoothing splines; extreme child poverty data; and data on acute viral infection of the respiratory system. excess of zeros. Only the Kulldorff scanning method identified the existence of a cluster, located and centered on the capital São Paulo. However, if a cluster is identified by the Kulldorff method in the presence of inflated and when not confirmed by the non-parametric approach, it is recommended that interpretations be performed with caution due to a high probability type error associated with Kulldorff method when model is not well specified. |
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CARVALHO, Daniel Matos dehttp://lattes.cnpq.br/5338448949047956http://lattes.cnpq.br/5519064508209103http://lattes.cnpq.br/7674916684282039DE BASTIANI, FernandaAMARAL, Getúlio José Amorim do2021-10-19T23:20:50Z2021-10-19T23:20:50Z2021-08-04CARVALHO, Daniel Matos de. Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape. 2021. Tese (Doutorado em Estatística) – Universidade Federal de Pernambuco, Recife, 2021.https://repositorio.ufpe.br/handle/123456789/41385This thesis presents two independent themes with different background. The first theme presents a new method for detecting spatial clusters, that is, a method for detecting regions with a high concentration of spatial phenomena, compared to a expected number, given a random distribution of events. The main contribution is to present a nonparametric method based on empirical likelihood functions, as an alternative to traditional methods of using clusters (scan). In this way, no distribution family is required for the variable of interest. To evaluate the method, simulation studies were carried out considering the zero-inflated poisson model, comparing the results with the scan method proposed by Kuldorff. The results show that the new method reduces the error probabilities of the type I for zero inflated, with low power for cluster with less than 8 locations. A study was carried out for Measles data in São Paulo, Brazil, which present a excess of zeros. Only the Kulldorff scanning method identified the existence of a cluster, located and centered on the capital São Paulo. However, if a cluster is identified by the Kulldorff method in the presence of inflated and when not confirmed by the non-parametric approach, it is recommended that interpretations be performed with caution due to a high probability type error associated with Kulldorff method when model is not well specified. The second theme aims to present two new approaches to robust estimation for generalized additive models of location, scale and shape - GAMLSS, which focus on contamination situations in the tails of distributions. The main motivation is the scarcity of robust methods for GAMLSS models. The thesis were subdivided into two topics. The first topic presents a proposal that seeks transformations in order to limit the influence function associated with the probability distribution of interest, modifying the logarithm structure of the likelihood function, using concepts of censorship. It also features: the robust GAMLSS method proposed by Rigby et al. (2019), considering the gamma distribution, presenting the bias corrections for the estimators; a modification of the method proposed by Rigby et al. (2019), considering the weight of observations in the estimation; and, finally, a large simulation study to evaluate the proposals, using the gamma distribution and contamination in the right tail of the distribution. The second topic is based on a simple adaptive truncation, where observations identified as possible outliers are verified and, if necessary, removed by truncation of the response variable distribution. The simulation studies used the gamma and beta distributions, left and right tail contamination, and three distinct models: parametric models with and without covariates and non-parametric models. The results show that, compared to existing methods in the literature, the truncated adaptive method has a better performance with lower mean square error and lower variability in most simulated scenarios. The overall performances of the proposals are illustrated through three applications: brain image resonance data, using bivariate smoothing splines; extreme child poverty data; and data on acute viral infection of the respiratory system. excess of zeros. Only the Kulldorff scanning method identified the existence of a cluster, located and centered on the capital São Paulo. However, if a cluster is identified by the Kulldorff method in the presence of inflated and when not confirmed by the non-parametric approach, it is recommended that interpretations be performed with caution due to a high probability type error associated with Kulldorff method when model is not well specified.Esta tese apresenta contribuições para três tópicos distintos sobre dois temas independentes. O primeiro tema apresenta um novo método para detecção de clusters espaciais, ou seja, um método para detecção de regiões com alta concentração de fenômenos espaciais, comparado com um número esperado, dada uma distribuição aleatória de eventos. A principal contribuição é apresentar um método não paramétrico baseado nas funções de verossimilhança empírica, como alternativa para métodos tradicionais de varredura de clusters (scan). Desta forma, nenhuma família de distribuição é exigida para a variável de interesse. Os resultados mostram que o novo método reduz as probabilidades de erro do tipo I para observações inflacionadas de zero, com baixo poder para cluster com menos de 8 localizações. Foi realizado um estudo para dados de Sarampo em São Paulo, Brasil, que apresentam um excesso de zeros. Apenas o método scan de Kulldorff identificou a existência de um cluster, localizado e centrado na capital São Paulo. Entretanto, caso seja identificado um cluster pelo método Kulldorff na presença de observações inflacionadas e quando não confirmado pela abordagem não paramétrica, é recomendável que as interpretações sejam realizadas com cautela devido a alta probabilidade do erro do tipo I associado ao método Kulldorff quando o modelo não é bem especificado. O segundo tema tem como objetivo apresentar duas novas abordagens para estimação robusta para os modelos GAMLSS, que focam em situações de contaminação nas caudas das distribuições, devido a escassez de métodos. A tese apresenta diversas contribuições para este tema, que foram subdivididas em dois tópicos. O primeiro tópico apresenta uma proposta que busca transformações de modo a limitar a função de influência associada a distribuição de probabilidade de interesse, modificando a estrutura do logaritmo da função de verossimilhança utilizando conceitos de censura. Apresenta ainda: o método robusto GAMLSS proposto por Rigby et al. (2019), considerando a distribuição gama, apresentando as correções de viés para o estimadores; uma modificação do método proposto por Rigby et al. (2019), considerando o peso das observações na estimação; e, por fim, um amplo estudo de simulação para avaliação das propostas, utilizando a distribuição gama e contaminações na cauda direita da distribuição. O segundo tópico baseia-se em um truncamento adaptativo simples, onde observações identificadas como possíveis outliers são verificadas e, se necessário, removidas por truncamento da distribuição da variável de resposta. Apresenta também uma proposta adaptativa para definição da constante de sintonia, necessária para estimação do modelo. Além de propor uma nova abordagem para modelagem robusta, comparamos com métodos disponíveis na literatura. Os estudos de simulação utilizaram as distribuições gama e beta, contaminações na cauda esquerda e direita, e três modelos distintos: modelos paramétricos sem e com covariáveis e modelos não paramétricos. Os resultados mostram que o método adaptativo truncado apresenta melhor desempenho com menores valores no erro quadrático médio e menor variabilidade na maioria dos cenários simulados. O desempenho das propostas é ilustrado por meio de três aplicações: dados de ressonância de imagens cerebrais, usando splines de suavização bivariadas; dados de extrema pobreza infantil; e a dados de infecção viral aguda do sistema respiratório.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em EstatisticaUFPEBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/embargoedAccessEstatística aplicadaDistribuiçãoSpatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shapeinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPEORIGINALTESE Daniel Matos de Carvalho.pdfTESE Daniel Matos de Carvalho.pdfapplication/pdf5281253https://repositorio.ufpe.br/bitstream/123456789/41385/1/TESE%20Daniel%20Matos%20de%20Carvalho.pdf473cb933bf5b4dff770f479281ca9cedMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv |
Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape |
title |
Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape |
spellingShingle |
Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape CARVALHO, Daniel Matos de Estatística aplicada Distribuição |
title_short |
Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape |
title_full |
Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape |
title_fullStr |
Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape |
title_full_unstemmed |
Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape |
title_sort |
Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape |
author |
CARVALHO, Daniel Matos de |
author_facet |
CARVALHO, Daniel Matos de |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/5338448949047956 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/5519064508209103 |
dc.contributor.advisor-coLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/7674916684282039 |
dc.contributor.author.fl_str_mv |
CARVALHO, Daniel Matos de |
dc.contributor.advisor1.fl_str_mv |
DE BASTIANI, Fernanda |
dc.contributor.advisor-co1.fl_str_mv |
AMARAL, Getúlio José Amorim do |
contributor_str_mv |
DE BASTIANI, Fernanda AMARAL, Getúlio José Amorim do |
dc.subject.por.fl_str_mv |
Estatística aplicada Distribuição |
topic |
Estatística aplicada Distribuição |
description |
This thesis presents two independent themes with different background. The first theme presents a new method for detecting spatial clusters, that is, a method for detecting regions with a high concentration of spatial phenomena, compared to a expected number, given a random distribution of events. The main contribution is to present a nonparametric method based on empirical likelihood functions, as an alternative to traditional methods of using clusters (scan). In this way, no distribution family is required for the variable of interest. To evaluate the method, simulation studies were carried out considering the zero-inflated poisson model, comparing the results with the scan method proposed by Kuldorff. The results show that the new method reduces the error probabilities of the type I for zero inflated, with low power for cluster with less than 8 locations. A study was carried out for Measles data in São Paulo, Brazil, which present a excess of zeros. Only the Kulldorff scanning method identified the existence of a cluster, located and centered on the capital São Paulo. However, if a cluster is identified by the Kulldorff method in the presence of inflated and when not confirmed by the non-parametric approach, it is recommended that interpretations be performed with caution due to a high probability type error associated with Kulldorff method when model is not well specified. The second theme aims to present two new approaches to robust estimation for generalized additive models of location, scale and shape - GAMLSS, which focus on contamination situations in the tails of distributions. The main motivation is the scarcity of robust methods for GAMLSS models. The thesis were subdivided into two topics. The first topic presents a proposal that seeks transformations in order to limit the influence function associated with the probability distribution of interest, modifying the logarithm structure of the likelihood function, using concepts of censorship. It also features: the robust GAMLSS method proposed by Rigby et al. (2019), considering the gamma distribution, presenting the bias corrections for the estimators; a modification of the method proposed by Rigby et al. (2019), considering the weight of observations in the estimation; and, finally, a large simulation study to evaluate the proposals, using the gamma distribution and contamination in the right tail of the distribution. The second topic is based on a simple adaptive truncation, where observations identified as possible outliers are verified and, if necessary, removed by truncation of the response variable distribution. The simulation studies used the gamma and beta distributions, left and right tail contamination, and three distinct models: parametric models with and without covariates and non-parametric models. The results show that, compared to existing methods in the literature, the truncated adaptive method has a better performance with lower mean square error and lower variability in most simulated scenarios. The overall performances of the proposals are illustrated through three applications: brain image resonance data, using bivariate smoothing splines; extreme child poverty data; and data on acute viral infection of the respiratory system. excess of zeros. Only the Kulldorff scanning method identified the existence of a cluster, located and centered on the capital São Paulo. However, if a cluster is identified by the Kulldorff method in the presence of inflated and when not confirmed by the non-parametric approach, it is recommended that interpretations be performed with caution due to a high probability type error associated with Kulldorff method when model is not well specified. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-10-19T23:20:50Z |
dc.date.available.fl_str_mv |
2021-10-19T23:20:50Z |
dc.date.issued.fl_str_mv |
2021-08-04 |
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 |
CARVALHO, Daniel Matos de. Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape. 2021. Tese (Doutorado em Estatística) – Universidade Federal de Pernambuco, Recife, 2021. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/41385 |
identifier_str_mv |
CARVALHO, Daniel Matos de. Spatial scan statistics based on empirical likelihood and robust fitting for generalized additive models for location, scale and shape. 2021. Tese (Doutorado em Estatística) – Universidade Federal de Pernambuco, Recife, 2021. |
url |
https://repositorio.ufpe.br/handle/123456789/41385 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/embargoedAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
embargoedAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Estatistica |
dc.publisher.initials.fl_str_mv |
UFPE |
dc.publisher.country.fl_str_mv |
Brasil |
publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFPE instname:Universidade Federal de Pernambuco (UFPE) instacron:UFPE |
instname_str |
Universidade Federal de Pernambuco (UFPE) |
instacron_str |
UFPE |
institution |
UFPE |
reponame_str |
Repositório Institucional da UFPE |
collection |
Repositório Institucional da UFPE |
bitstream.url.fl_str_mv |
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