Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations

Autores
Giménez, Patricia; López, Jorge N.; Guarracino, Lucas Gastón
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study the geometry of the differentiable manifold associated with two samples of symmetric distributions in the real line equipped with the Fisher information as Riemannian metric. Expressions for the entries of the information matrix are obtained under different assumptions. The geodesic or Rao distance induced by this geometry is used to construct asymptotic parametrization-invariant testing procedures for comparing location parameters. As special cases, we obtain new asymptotic tests for the two sample Behrens-Fisher and Fieller-Creasy problems. Testing equality of several location parameters is also considered. It is shown that when scale parameters are equal, the geodesic test statistic is a strictly monotone increasing function of the Wald statistic. Empirical results for the Student-t distribution provide evidence that the geodesic test statistic has good sampling properties in terms of level and power.
Fil: Giménez, Patricia. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: López, Jorge N.. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Guarracino, Lucas Gastón. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Statistical Manifolds
Fisher Information
Geodesic Distance
Hypothesis Testing
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:11336/38043
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/38043
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical PopulationsGiménez, PatriciaLópez, Jorge N.Guarracino, Lucas GastónStatistical ManifoldsFisher InformationGeodesic DistanceHypothesis Testinghttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study the geometry of the differentiable manifold associated with two samples of symmetric distributions in the real line equipped with the Fisher information as Riemannian metric. Expressions for the entries of the information matrix are obtained under different assumptions. The geodesic or Rao distance induced by this geometry is used to construct asymptotic parametrization-invariant testing procedures for comparing location parameters. As special cases, we obtain new asymptotic tests for the two sample Behrens-Fisher and Fieller-Creasy problems. Testing equality of several location parameters is also considered. It is shown that when scale parameters are equal, the geodesic test statistic is a strictly monotone increasing function of the Wald statistic. Empirical results for the Student-t distribution provide evidence that the geodesic test statistic has good sampling properties in terms of level and power.Fil: Giménez, Patricia. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: López, Jorge N.. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Guarracino, Lucas Gastón. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer India2016-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/38043Giménez, Patricia; López, Jorge N.; Guarracino, Lucas Gastón; Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations; Springer India; Sankhya A; 78; 1; 2-2016; 19-420976-836X0976-8378CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s13171-015-0068-5info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs13171-015-0068-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:40:49Zoai:ri.conicet.gov.ar:11336/38043instacron: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 09:40:49.501CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations
title Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations
spellingShingle Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations
Giménez, Patricia
Statistical Manifolds
Fisher Information
Geodesic Distance
Hypothesis Testing
title_short Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations
title_full Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations
title_fullStr Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations
title_full_unstemmed Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations
title_sort Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations
dc.creator.none.fl_str_mv Giménez, Patricia
López, Jorge N.
Guarracino, Lucas Gastón
author Giménez, Patricia
author_facet Giménez, Patricia
López, Jorge N.
Guarracino, Lucas Gastón
author_role author
author2 López, Jorge N.
Guarracino, Lucas Gastón
author2_role author
author
dc.subject.none.fl_str_mv Statistical Manifolds
Fisher Information
Geodesic Distance
Hypothesis Testing
topic Statistical Manifolds
Fisher Information
Geodesic Distance
Hypothesis Testing
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we study the geometry of the differentiable manifold associated with two samples of symmetric distributions in the real line equipped with the Fisher information as Riemannian metric. Expressions for the entries of the information matrix are obtained under different assumptions. The geodesic or Rao distance induced by this geometry is used to construct asymptotic parametrization-invariant testing procedures for comparing location parameters. As special cases, we obtain new asymptotic tests for the two sample Behrens-Fisher and Fieller-Creasy problems. Testing equality of several location parameters is also considered. It is shown that when scale parameters are equal, the geodesic test statistic is a strictly monotone increasing function of the Wald statistic. Empirical results for the Student-t distribution provide evidence that the geodesic test statistic has good sampling properties in terms of level and power.
Fil: Giménez, Patricia. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: López, Jorge N.. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Guarracino, Lucas Gastón. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this paper we study the geometry of the differentiable manifold associated with two samples of symmetric distributions in the real line equipped with the Fisher information as Riemannian metric. Expressions for the entries of the information matrix are obtained under different assumptions. The geodesic or Rao distance induced by this geometry is used to construct asymptotic parametrization-invariant testing procedures for comparing location parameters. As special cases, we obtain new asymptotic tests for the two sample Behrens-Fisher and Fieller-Creasy problems. Testing equality of several location parameters is also considered. It is shown that when scale parameters are equal, the geodesic test statistic is a strictly monotone increasing function of the Wald statistic. Empirical results for the Student-t distribution provide evidence that the geodesic test statistic has good sampling properties in terms of level and power.
publishDate 2016
dc.date.none.fl_str_mv 2016-02
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/11336/38043
Giménez, Patricia; López, Jorge N.; Guarracino, Lucas Gastón; Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations; Springer India; Sankhya A; 78; 1; 2-2016; 19-42
0976-836X
0976-8378
CONICET Digital
CONICET
url http://hdl.handle.net/11336/38043
identifier_str_mv Giménez, Patricia; López, Jorge N.; Guarracino, Lucas Gastón; Geodesic Hypothesis Testing for Comparing Location Parameters in Elliptical Populations; Springer India; Sankhya A; 78; 1; 2-2016; 19-42
0976-836X
0976-8378
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s13171-015-0068-5
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs13171-015-0068-5
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 Springer India
publisher.none.fl_str_mv Springer India
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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