Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection

Autores
Bianco, Ana Maria; Boente Boente, Graciela Lina; Rodrigues, Isabel
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
When dealing with situations in which the responses are discrete or show some type of asymmetry, the linear model is not appropriate to establish the relation between the responses and the covariates. Generalized linear models serve this purpose, since they allow one to model the mean of the responses through a link function, linearly on the covariates. When atypical observations are present in the sample, robust estimators are useful to provide fair estimations as well as to build outlier detection rules. The focus of this paper is to define robust estimators for the regression parameter when missing data possibly occur in the responses. The estimators introduced turn out to be consistent under mild conditions. In particular, resistant methods for Poisson and Gamma models are given. A simulation study allows one to compare the behaviour of the classical and robust estimators, under different contamination schemes. The robustness of the proposed procedures is studied through the influence function, while asymptotic variances are derived from it. Besides, outlier detection rules are defined using the influence function. The procedure is also illustrated by analysing a real data set.
Fil: Bianco, Ana Maria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Boente Boente, Graciela Lina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rodrigues, Isabel. Technical University of Lisbon; Portugal
Materia
Fisher-Consistency
Generalized Lnear Model
Missing Data
Outliers
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/15863
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/15863
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detectionBianco, Ana MariaBoente Boente, Graciela LinaRodrigues, IsabelFisher-ConsistencyGeneralized Lnear ModelMissing DataOutliershttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1When dealing with situations in which the responses are discrete or show some type of asymmetry, the linear model is not appropriate to establish the relation between the responses and the covariates. Generalized linear models serve this purpose, since they allow one to model the mean of the responses through a link function, linearly on the covariates. When atypical observations are present in the sample, robust estimators are useful to provide fair estimations as well as to build outlier detection rules. The focus of this paper is to define robust estimators for the regression parameter when missing data possibly occur in the responses. The estimators introduced turn out to be consistent under mild conditions. In particular, resistant methods for Poisson and Gamma models are given. A simulation study allows one to compare the behaviour of the classical and robust estimators, under different contamination schemes. The robustness of the proposed procedures is studied through the influence function, while asymptotic variances are derived from it. Besides, outlier detection rules are defined using the influence function. The procedure is also illustrated by analysing a real data set.Fil: Bianco, Ana Maria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Boente Boente, Graciela Lina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rodrigues, Isabel. Technical University of Lisbon; PortugalElsevier Inc2013-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15863Bianco, Ana Maria; Boente Boente, Graciela Lina; Rodrigues, Isabel; Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection; Elsevier Inc; Journal Of Multivariate Analysis; 114; 2-2013; 209-2260047-259Xenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmva.2012.08.008info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0047259X12002060info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:28:39Zoai:ri.conicet.gov.ar:11336/15863instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:28:39.75CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection
title Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection
spellingShingle Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection
Bianco, Ana Maria
Fisher-Consistency
Generalized Lnear Model
Missing Data
Outliers
title_short Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection
title_full Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection
title_fullStr Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection
title_full_unstemmed Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection
title_sort Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection
dc.creator.none.fl_str_mv Bianco, Ana Maria
Boente Boente, Graciela Lina
Rodrigues, Isabel
author Bianco, Ana Maria
author_facet Bianco, Ana Maria
Boente Boente, Graciela Lina
Rodrigues, Isabel
author_role author
author2 Boente Boente, Graciela Lina
Rodrigues, Isabel
author2_role author
author
dc.subject.none.fl_str_mv Fisher-Consistency
Generalized Lnear Model
Missing Data
Outliers
topic Fisher-Consistency
Generalized Lnear Model
Missing Data
Outliers
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv When dealing with situations in which the responses are discrete or show some type of asymmetry, the linear model is not appropriate to establish the relation between the responses and the covariates. Generalized linear models serve this purpose, since they allow one to model the mean of the responses through a link function, linearly on the covariates. When atypical observations are present in the sample, robust estimators are useful to provide fair estimations as well as to build outlier detection rules. The focus of this paper is to define robust estimators for the regression parameter when missing data possibly occur in the responses. The estimators introduced turn out to be consistent under mild conditions. In particular, resistant methods for Poisson and Gamma models are given. A simulation study allows one to compare the behaviour of the classical and robust estimators, under different contamination schemes. The robustness of the proposed procedures is studied through the influence function, while asymptotic variances are derived from it. Besides, outlier detection rules are defined using the influence function. The procedure is also illustrated by analysing a real data set.
Fil: Bianco, Ana Maria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Boente Boente, Graciela Lina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rodrigues, Isabel. Technical University of Lisbon; Portugal
description When dealing with situations in which the responses are discrete or show some type of asymmetry, the linear model is not appropriate to establish the relation between the responses and the covariates. Generalized linear models serve this purpose, since they allow one to model the mean of the responses through a link function, linearly on the covariates. When atypical observations are present in the sample, robust estimators are useful to provide fair estimations as well as to build outlier detection rules. The focus of this paper is to define robust estimators for the regression parameter when missing data possibly occur in the responses. The estimators introduced turn out to be consistent under mild conditions. In particular, resistant methods for Poisson and Gamma models are given. A simulation study allows one to compare the behaviour of the classical and robust estimators, under different contamination schemes. The robustness of the proposed procedures is studied through the influence function, while asymptotic variances are derived from it. Besides, outlier detection rules are defined using the influence function. The procedure is also illustrated by analysing a real data set.
publishDate 2013
dc.date.none.fl_str_mv 2013-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/15863
Bianco, Ana Maria; Boente Boente, Graciela Lina; Rodrigues, Isabel; Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection; Elsevier Inc; Journal Of Multivariate Analysis; 114; 2-2013; 209-226
0047-259X
url http://hdl.handle.net/11336/15863
identifier_str_mv Bianco, Ana Maria; Boente Boente, Graciela Lina; Rodrigues, Isabel; Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection; Elsevier Inc; Journal Of Multivariate Analysis; 114; 2-2013; 209-226
0047-259X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmva.2012.08.008
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0047259X12002060
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Inc
publisher.none.fl_str_mv Elsevier Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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