Visual tools to identify influential observations in spatial data
Main Author: | |
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Publication Date: | 2021 |
Format: | Master thesis |
Language: | eng |
Source: | Repositório Institucional da UFPE |
Download full: | https://repositorio.ufpe.br/handle/123456789/43661 |
Summary: | We adapted the hair-plot, proposed by Genton and Ruiz-Gazen (2010), to identify and vi- sualize influential observations in spatial data. Three graphic tools were created: the bihair-plot, the principal components hair-plot and functional hair-plot. The first tool depict trajectories of the values of a spatial semivariance estimator when adding a perturbation to each observation of a vector of spatial data observed considering two lags. The second describes trajectories of the principal components of a spatial semivariance estimator values for all lags when each observation of data is perturbed, making it possible to identify influential observations in spa- tial data containing as much information as possible from the data set. The third is obtained from the values of the trace-semivariogram estimator when the data receive a disturbance. The estimators considered in the study were the sample semivariogram for univariate case, sample cross-semivariogram for bivariate case and sample trace-semivariogram for functional data. Another method used to obtain the cross-semivariogram was Minimum Volume Ellipsoid, which is more sensitive to outliers. Based on this, we observed that it is not possible to detect influential observations. We defined the quadratic form of the estimators and the influence function, in order to understand their behavior and properties. Finally, we make an application with these tools in the pollution data for the univariate case, complementing the results shown in Genton and Ruiz-Gazen (2010), the meuse data from the sp package for the bivariate case and average temperatures from the geofd package for the functional case. |
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OLIVEIRA, Isabel Soares Diniz dehttp://lattes.cnpq.br/2198421357007814http://lattes.cnpq.br/5519064508209103DE BASTIANI, Fernanda2022-04-04T13:16:04Z2022-04-04T13:16:04Z2021-10-28OLIVEIRA, Isabel Soares Diniz de. Visual tools to identify influential observations in spatial data. 2021. Dissertação (Mestrado em Estatística) - Universidade Federal de Pernambuco, Recife, 2021.https://repositorio.ufpe.br/handle/123456789/43661We adapted the hair-plot, proposed by Genton and Ruiz-Gazen (2010), to identify and vi- sualize influential observations in spatial data. Three graphic tools were created: the bihair-plot, the principal components hair-plot and functional hair-plot. The first tool depict trajectories of the values of a spatial semivariance estimator when adding a perturbation to each observation of a vector of spatial data observed considering two lags. The second describes trajectories of the principal components of a spatial semivariance estimator values for all lags when each observation of data is perturbed, making it possible to identify influential observations in spa- tial data containing as much information as possible from the data set. The third is obtained from the values of the trace-semivariogram estimator when the data receive a disturbance. The estimators considered in the study were the sample semivariogram for univariate case, sample cross-semivariogram for bivariate case and sample trace-semivariogram for functional data. Another method used to obtain the cross-semivariogram was Minimum Volume Ellipsoid, which is more sensitive to outliers. Based on this, we observed that it is not possible to detect influential observations. We defined the quadratic form of the estimators and the influence function, in order to understand their behavior and properties. Finally, we make an application with these tools in the pollution data for the univariate case, complementing the results shown in Genton and Ruiz-Gazen (2010), the meuse data from the sp package for the bivariate case and average temperatures from the geofd package for the functional case.Adaptamos o hair-plot, proposto por Genton and Ruiz-Gazen (2010), para identificar e visualizar observações influentes em dados espaciais. Três ferramentas gráficas foram criadas: o bihair-plot, os principais componentes do hair-plot e o hair-plot funcional. A primeira ferra- menta descreve trajetórias dos valores de um estimador de semivariância espacial ao adicionar uma perturbação a cada observação de um vetor de dados espaciais observado considerando dois lags. O segundo descreve as trajetórias dos componentes principais de um estimador de semivariância espacial para todos os lags quando cada observação de dados é perturbada, tornando possível identificar observações influentes em dados espaciais contendo o máximo de informações possível do conjunto de dados. O terceiro é obtido a partir dos valores do esti- mador do trace-semivariogram quando os dados recebem uma perturbação. Os estimadores considerados no estudo foram o semivariograma de amostra para caso univariado, semivario- grama cruzado de amostra para caso bivariado e trace-semivariograma amostral para dados funcionais. Outro método utilizado para obter o semivariograma cruzado foi o Elipsóide de Volume Mínimo, que é mais sensível a outliers. Com base nisso, observamos que não é possí- vel detectar observações influentes. Definimos a forma quadrática dos estimadores e a função de influência, a fim de compreender seu comportamento e propriedades. Finalmente, fazemos uma aplicação com essas ferramentas nos dados de poluição para o caso univariado, comple- mentando os resultados mostrados em Genton and Ruiz-Gazen (2010), os dados meuse do pacote sp para o caso bivariado e dados de temperaturas médias do pacote geofd para o caso funcional, inicialmente obtidas do Serviço Meteorológico do Canadá.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em EstatisticaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/embargoedAccessEstatística AplicadaAnálise de dados funcionaisDados espaciais influentesSemivariogramaVisual tools to identify influential observations in spatial datainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPEORIGINALDISSERTAÇÃO Isabel Soares Diniz de Oliveira.pdfDISSERTAÇÃO Isabel Soares Diniz de Oliveira.pdfapplication/pdf1605687https://repositorio.ufpe.br/bitstream/123456789/43661/1/DISSERTA%c3%87%c3%83O%20Isabel%20Soares%20Diniz%20de%20Oliveira.pdf412b65576bd698d4075da0d250ec6941MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv |
Visual tools to identify influential observations in spatial data |
title |
Visual tools to identify influential observations in spatial data |
spellingShingle |
Visual tools to identify influential observations in spatial data OLIVEIRA, Isabel Soares Diniz de Estatística Aplicada Análise de dados funcionais Dados espaciais influentes Semivariograma |
title_short |
Visual tools to identify influential observations in spatial data |
title_full |
Visual tools to identify influential observations in spatial data |
title_fullStr |
Visual tools to identify influential observations in spatial data |
title_full_unstemmed |
Visual tools to identify influential observations in spatial data |
title_sort |
Visual tools to identify influential observations in spatial data |
author |
OLIVEIRA, Isabel Soares Diniz de |
author_facet |
OLIVEIRA, Isabel Soares Diniz de |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/2198421357007814 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/5519064508209103 |
dc.contributor.author.fl_str_mv |
OLIVEIRA, Isabel Soares Diniz de |
dc.contributor.advisor1.fl_str_mv |
DE BASTIANI, Fernanda |
contributor_str_mv |
DE BASTIANI, Fernanda |
dc.subject.por.fl_str_mv |
Estatística Aplicada Análise de dados funcionais Dados espaciais influentes Semivariograma |
topic |
Estatística Aplicada Análise de dados funcionais Dados espaciais influentes Semivariograma |
description |
We adapted the hair-plot, proposed by Genton and Ruiz-Gazen (2010), to identify and vi- sualize influential observations in spatial data. Three graphic tools were created: the bihair-plot, the principal components hair-plot and functional hair-plot. The first tool depict trajectories of the values of a spatial semivariance estimator when adding a perturbation to each observation of a vector of spatial data observed considering two lags. The second describes trajectories of the principal components of a spatial semivariance estimator values for all lags when each observation of data is perturbed, making it possible to identify influential observations in spa- tial data containing as much information as possible from the data set. The third is obtained from the values of the trace-semivariogram estimator when the data receive a disturbance. The estimators considered in the study were the sample semivariogram for univariate case, sample cross-semivariogram for bivariate case and sample trace-semivariogram for functional data. Another method used to obtain the cross-semivariogram was Minimum Volume Ellipsoid, which is more sensitive to outliers. Based on this, we observed that it is not possible to detect influential observations. We defined the quadratic form of the estimators and the influence function, in order to understand their behavior and properties. Finally, we make an application with these tools in the pollution data for the univariate case, complementing the results shown in Genton and Ruiz-Gazen (2010), the meuse data from the sp package for the bivariate case and average temperatures from the geofd package for the functional case. |
publishDate |
2021 |
dc.date.issued.fl_str_mv |
2021-10-28 |
dc.date.accessioned.fl_str_mv |
2022-04-04T13:16:04Z |
dc.date.available.fl_str_mv |
2022-04-04T13:16:04Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
OLIVEIRA, Isabel Soares Diniz de. Visual tools to identify influential observations in spatial data. 2021. Dissertação (Mestrado em Estatística) - Universidade Federal de Pernambuco, Recife, 2021. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/43661 |
identifier_str_mv |
OLIVEIRA, Isabel Soares Diniz de. Visual tools to identify influential observations in spatial data. 2021. Dissertação (Mestrado em Estatística) - Universidade Federal de Pernambuco, Recife, 2021. |
url |
https://repositorio.ufpe.br/handle/123456789/43661 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/embargoedAccess |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil 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 |
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Repositório Institucional da UFPE |
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