Objective Bayesian point and region estimation in location-scale models

Point and region estimation may both be described as specific decision problems. In point estimation,the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution t...

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Detalles Bibliográficos
Autor: Bernardo, José Miguel
Tipo de recurso: artículo
Fecha de publicación:2007
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2099/3807
Acceso en línea:https://hdl.handle.net/2099/3807
Access Level:acceso abierto
Palabra clave:Statistics
Decision theory
Inference
Estadística
Teoria de la decisió
Inferència
Classificació AMS::62 Statistics::62B Sufficiency and information
Classificació AMS::62 Statistics::62C Decision theory
Classificació AMS::62 Statistics::62F Parametric inference
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spelling Objective Bayesian point and region estimation in location-scale modelsBernardo, José MiguelStatisticsDecision theoryInferenceEstadísticaTeoria de la decisióInferènciaClassificació AMS::62 Statistics::62B Sufficiency and informationClassificació AMS::62 Statistics::62C Decision theoryClassificació AMS::62 Statistics::62F Parametric inferencePoint and region estimation may both be described as specific decision problems. In point estimation,the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution to these decision problems must depend on both the utility function and the prior distribution. Estimators intended for general use should surely be invariant under one-to-one transformations, and this requires the use of an invariant loss function; moreover, an objective solution requires the use of a prior which does not introduce subjective elements. The combined use of an invariant information-theory based loss function, the intrinsic discrepancy, and an objective prior, the reference prior, produces a general solution to both point and region estimation problems. In this paper, estimation of the two parameters of univariate location-scale models is considered in detail from this point of view, with special attention to the normal model. The solutions found are compared with a range of conventional solutions.Peer ReviewedInstitut d'Estadística de Catalunya20072007-01-0120072007-11-16journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2099/3807reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 2.5 Spainhttp://creativecommons.org/licenses/by-nc-nd/2.5/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2099/38072026-05-27T15:37:01Z
dc.title.none.fl_str_mv Objective Bayesian point and region estimation in location-scale models
title Objective Bayesian point and region estimation in location-scale models
spellingShingle Objective Bayesian point and region estimation in location-scale models
Bernardo, José Miguel
Statistics
Decision theory
Inference
Estadística
Teoria de la decisió
Inferència
Classificació AMS::62 Statistics::62B Sufficiency and information
Classificació AMS::62 Statistics::62C Decision theory
Classificació AMS::62 Statistics::62F Parametric inference
title_short Objective Bayesian point and region estimation in location-scale models
title_full Objective Bayesian point and region estimation in location-scale models
title_fullStr Objective Bayesian point and region estimation in location-scale models
title_full_unstemmed Objective Bayesian point and region estimation in location-scale models
title_sort Objective Bayesian point and region estimation in location-scale models
dc.creator.none.fl_str_mv Bernardo, José Miguel
author Bernardo, José Miguel
author_facet Bernardo, José Miguel
author_role author
dc.subject.none.fl_str_mv Statistics
Decision theory
Inference
Estadística
Teoria de la decisió
Inferència
Classificació AMS::62 Statistics::62B Sufficiency and information
Classificació AMS::62 Statistics::62C Decision theory
Classificació AMS::62 Statistics::62F Parametric inference
topic Statistics
Decision theory
Inference
Estadística
Teoria de la decisió
Inferència
Classificació AMS::62 Statistics::62B Sufficiency and information
Classificació AMS::62 Statistics::62C Decision theory
Classificació AMS::62 Statistics::62F Parametric inference
description Point and region estimation may both be described as specific decision problems. In point estimation,the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution to these decision problems must depend on both the utility function and the prior distribution. Estimators intended for general use should surely be invariant under one-to-one transformations, and this requires the use of an invariant loss function; moreover, an objective solution requires the use of a prior which does not introduce subjective elements. The combined use of an invariant information-theory based loss function, the intrinsic discrepancy, and an objective prior, the reference prior, produces a general solution to both point and region estimation problems. In this paper, estimation of the two parameters of univariate location-scale models is considered in detail from this point of view, with special attention to the normal model. The solutions found are compared with a range of conventional solutions.
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-01-01
2007
2007-11-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2099/3807
url https://hdl.handle.net/2099/3807
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Institut d'Estadística de Catalunya
publisher.none.fl_str_mv Institut d'Estadística de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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