On the mean and variance of the generalized inverse of a singular wishart matrix

Autores
Cook, R. Dennis; Forzani, Liliana Maria
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We derive the first and the second moments of the Moore- Penrose generalized inverse of a singular standard Wishart matrix without relying on a density. Instead, we use the moments of an inverse Wishart distribution and an invariance argument which is related to the literature on tensor functions. We also find the order of the spectral norm of the generalized inverse of a Wishart matrix as its dimension and degrees of freedom diverge.
Fil: Cook, R. Dennis. University of Minnesota; Estados Unidos
Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
Inverse Wishart Distribution
Moore-Penrose Generalized Inverse
Singular Inversewishart Distributions
Tensor Functions
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:11336/75177
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/75177
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network_name_str CONICET Digital (CONICET)
spelling On the mean and variance of the generalized inverse of a singular wishart matrixCook, R. DennisForzani, Liliana MariaInverse Wishart DistributionMoore-Penrose Generalized InverseSingular Inversewishart DistributionsTensor Functionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We derive the first and the second moments of the Moore- Penrose generalized inverse of a singular standard Wishart matrix without relying on a density. Instead, we use the moments of an inverse Wishart distribution and an invariance argument which is related to the literature on tensor functions. We also find the order of the spectral norm of the generalized inverse of a Wishart matrix as its dimension and degrees of freedom diverge.Fil: Cook, R. Dennis. University of Minnesota; Estados UnidosFil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaInstitute of Mathematical Statistics2011-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/75177Cook, R. Dennis; Forzani, Liliana Maria; On the mean and variance of the generalized inverse of a singular wishart matrix; Institute of Mathematical Statistics; Electronic Journal of Statistics; 5; 1-2011; 146-1581935-7524CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.ejs/1300198786&view=body&content-type=pdfview_1info:eu-repo/semantics/altIdentifier/doi/10.1214/11-EJS602info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:56:00Zoai:ri.conicet.gov.ar:11336/75177instacron: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 09:56:00.921CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the mean and variance of the generalized inverse of a singular wishart matrix
title On the mean and variance of the generalized inverse of a singular wishart matrix
spellingShingle On the mean and variance of the generalized inverse of a singular wishart matrix
Cook, R. Dennis
Inverse Wishart Distribution
Moore-Penrose Generalized Inverse
Singular Inversewishart Distributions
Tensor Functions
title_short On the mean and variance of the generalized inverse of a singular wishart matrix
title_full On the mean and variance of the generalized inverse of a singular wishart matrix
title_fullStr On the mean and variance of the generalized inverse of a singular wishart matrix
title_full_unstemmed On the mean and variance of the generalized inverse of a singular wishart matrix
title_sort On the mean and variance of the generalized inverse of a singular wishart matrix
dc.creator.none.fl_str_mv Cook, R. Dennis
Forzani, Liliana Maria
author Cook, R. Dennis
author_facet Cook, R. Dennis
Forzani, Liliana Maria
author_role author
author2 Forzani, Liliana Maria
author2_role author
dc.subject.none.fl_str_mv Inverse Wishart Distribution
Moore-Penrose Generalized Inverse
Singular Inversewishart Distributions
Tensor Functions
topic Inverse Wishart Distribution
Moore-Penrose Generalized Inverse
Singular Inversewishart Distributions
Tensor Functions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We derive the first and the second moments of the Moore- Penrose generalized inverse of a singular standard Wishart matrix without relying on a density. Instead, we use the moments of an inverse Wishart distribution and an invariance argument which is related to the literature on tensor functions. We also find the order of the spectral norm of the generalized inverse of a Wishart matrix as its dimension and degrees of freedom diverge.
Fil: Cook, R. Dennis. University of Minnesota; Estados Unidos
Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description We derive the first and the second moments of the Moore- Penrose generalized inverse of a singular standard Wishart matrix without relying on a density. Instead, we use the moments of an inverse Wishart distribution and an invariance argument which is related to the literature on tensor functions. We also find the order of the spectral norm of the generalized inverse of a Wishart matrix as its dimension and degrees of freedom diverge.
publishDate 2011
dc.date.none.fl_str_mv 2011-01
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/11336/75177
Cook, R. Dennis; Forzani, Liliana Maria; On the mean and variance of the generalized inverse of a singular wishart matrix; Institute of Mathematical Statistics; Electronic Journal of Statistics; 5; 1-2011; 146-158
1935-7524
CONICET Digital
CONICET
url http://hdl.handle.net/11336/75177
identifier_str_mv Cook, R. Dennis; Forzani, Liliana Maria; On the mean and variance of the generalized inverse of a singular wishart matrix; Institute of Mathematical Statistics; Electronic Journal of Statistics; 5; 1-2011; 146-158
1935-7524
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.ejs/1300198786&view=body&content-type=pdfview_1
info:eu-repo/semantics/altIdentifier/doi/10.1214/11-EJS602
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 Institute of Mathematical Statistics
publisher.none.fl_str_mv Institute of Mathematical Statistics
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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