Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects

Estimating a variance component in the model of analysis of variance with random effects and testing the hypothesis that the variance vanishes are important issues in many applications. Such inferences are beyond the confines of the standard (asymptotic) theory because a zero variance is on the boun...

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Autores:
Longford, Nicholas T.
Andrade, Mercedes
Tipo de recurso:
Article of journal
Fecha de publicación:
2015
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66548
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66548
http://bdigital.unal.edu.co/67576/
Palabra clave:
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Analysis of Variance with Random Effects
Decision
Equilibrium
Expected Loss
Variance Ratio
Análisis de varianza con efectos aleatorios
Decisión
Equilibrio
Pérdida esperada
Tazón de la varianza.
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Longford, Nicholas T.2f690827-841e-46e9-8887-b358ef8bab28300Andrade, Mercedes80e0ec55-1143-4c10-bf36-b40ad29b9b543002019-07-03T02:20:58Z2019-07-03T02:20:58Z2015-01-01ISSN: 2389-8976https://repositorio.unal.edu.co/handle/unal/66548http://bdigital.unal.edu.co/67576/Estimating a variance component in the model of analysis of variance with random effects and testing the hypothesis that the variance vanishes are important issues in many applications. Such inferences are beyond the confines of the standard (asymptotic) theory because a zero variance is on the boundary of the parameter space and the maximum likelihood or another reasonable estimator of variance has a non-trivial probability of zero in many settings. We derive decision rules regarding the variance ratio in balanced one-way analysis of variance, in both the frequentist and Bayesian perspectives. We argue that this approach is superior to hypothesis testing because it incorporates the consequences of the two kinds of error (incorrect choice) that may be committed. An application to a track athlete’s training performance is presented.La estimación de una de las varianzas en el modelo de análisis de la varianza con efectos aleatorios y la prueba de hipótesis de que la varianza se anula, son temas importantes en muchas aplicaciones. Tales inferencias están fuera de los confines de la teoría asintótica estándar porque una varianza cero está en la frontera del espacio paramétrico y la máxima verosimilitud u otro estimador razonable de una varianza tiene una probabilidad no trivial de cero en muchos contextos. Nosotros derivamos una regla de decisión sobre la razón de varianzas en un análisis de varianza de un factor balanceado tanto para la perspectiva frecuentista como la Bayesiana. Argumentamos que este enfoque es superior a la prueba de hipótesis porque incorpora las consecuencias de los dos tipos de error (elección incorrecta) que pueden cometerse. Se presenta una aplicación sobre los rendimientos de los entrenamientos de un atleta de pista.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadísticahttps://revistas.unal.edu.co/index.php/estad/article/view/48810Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de EstadísticaRevista Colombiana de EstadísticaLongford, Nicholas T. and Andrade, Mercedes (2015) Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects. Revista Colombiana de Estadística, 38 (1). pp. 181-207. ISSN 2389-897651 Matemáticas / Mathematics31 Colecciones de estadística general / StatisticsAnalysis of Variance with Random EffectsDecisionEquilibriumExpected LossVariance RatioAnálisis de varianza con efectos aleatoriosDecisiónEquilibrioPérdida esperadaTazón de la varianza.Decision Theory for the Variance Ratio in One-Way ANOVA with Random EffectsArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL48810-239287-1-PB.pdfapplication/pdf1435707https://repositorio.unal.edu.co/bitstream/unal/66548/1/48810-239287-1-PB.pdf146a189cb7f221aaf60882291729637cMD51THUMBNAIL48810-239287-1-PB.pdf.jpg48810-239287-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg5357https://repositorio.unal.edu.co/bitstream/unal/66548/2/48810-239287-1-PB.pdf.jpg43f8b47f2f1fece626bf3209d7d42fcbMD52unal/66548oai:repositorio.unal.edu.co:unal/665482023-05-25 23:03:10.621Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects
title Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects
spellingShingle Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Analysis of Variance with Random Effects
Decision
Equilibrium
Expected Loss
Variance Ratio
Análisis de varianza con efectos aleatorios
Decisión
Equilibrio
Pérdida esperada
Tazón de la varianza.
title_short Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects
title_full Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects
title_fullStr Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects
title_full_unstemmed Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects
title_sort Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects
dc.creator.fl_str_mv Longford, Nicholas T.
Andrade, Mercedes
dc.contributor.author.spa.fl_str_mv Longford, Nicholas T.
Andrade, Mercedes
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
topic 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Analysis of Variance with Random Effects
Decision
Equilibrium
Expected Loss
Variance Ratio
Análisis de varianza con efectos aleatorios
Decisión
Equilibrio
Pérdida esperada
Tazón de la varianza.
dc.subject.proposal.spa.fl_str_mv Analysis of Variance with Random Effects
Decision
Equilibrium
Expected Loss
Variance Ratio
Análisis de varianza con efectos aleatorios
Decisión
Equilibrio
Pérdida esperada
Tazón de la varianza.
description Estimating a variance component in the model of analysis of variance with random effects and testing the hypothesis that the variance vanishes are important issues in many applications. Such inferences are beyond the confines of the standard (asymptotic) theory because a zero variance is on the boundary of the parameter space and the maximum likelihood or another reasonable estimator of variance has a non-trivial probability of zero in many settings. We derive decision rules regarding the variance ratio in balanced one-way analysis of variance, in both the frequentist and Bayesian perspectives. We argue that this approach is superior to hypothesis testing because it incorporates the consequences of the two kinds of error (incorrect choice) that may be committed. An application to a track athlete’s training performance is presented.
publishDate 2015
dc.date.issued.spa.fl_str_mv 2015-01-01
dc.date.accessioned.spa.fl_str_mv 2019-07-03T02:20:58Z
dc.date.available.spa.fl_str_mv 2019-07-03T02:20:58Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv ISSN: 2389-8976
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/66548
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/67576/
identifier_str_mv ISSN: 2389-8976
url https://repositorio.unal.edu.co/handle/unal/66548
http://bdigital.unal.edu.co/67576/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/estad/article/view/48810
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Estadística
Revista Colombiana de Estadística
dc.relation.references.spa.fl_str_mv Longford, Nicholas T. and Andrade, Mercedes (2015) Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects. Revista Colombiana de Estadística, 38 (1). pp. 181-207. ISSN 2389-8976
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadística
institution Universidad Nacional de Colombia
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