Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions

In this paper, we establish a connection between the Hadamard product and the usual matrix multiplication. In addition, we study some new properties of the Hadamard product and explore the inverse problem associated with the established connection, which facilitates diverse applications. Furthermore...

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Fecha de publicación:
2012
Institución:
Universidad de Medellín
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Repositorio UDEM
Idioma:
eng
OAI Identifier:
oai:repository.udem.edu.co:11407/1363
Acceso en línea:
http://hdl.handle.net/11407/1363
Palabra clave:
Generalized birnbaum-saunders distribution
Kronecker product
Multivariate analysis
Schur or entry-wise product
Shape theory
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restrictedAccess
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http://purl.org/coar/access_right/c_16ec
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spelling 2015-10-09T13:17:52Z2015-10-09T13:17:52Z20120047259Xhttp://hdl.handle.net/11407/136310.1016/j.jmva.2011.07.004In this paper, we establish a connection between the Hadamard product and the usual matrix multiplication. In addition, we study some new properties of the Hadamard product and explore the inverse problem associated with the established connection, which facilitates diverse applications. Furthermore, we propose a matrix-variate generalized Birnbaum–Saunders (GBS) distribution. Three representations of the matrix-variate GBS density are provided, one of them by using the mentioned connection. The main motivation of this article is based on the fact that the representation of the matrix-variate GBS density based on element-by-element specification does not allow matrix transformations. Consequently, some statistical procedures based on this representation, such as multivariate data analysis and statistical shape theory, cannot be performed. For this reason, the primary goal of this work is to obtain a matrix representation of the matrix-variate GBS density that is useful for some statistical applications. When the GBS density is expressed by means of a matrix representation based on the Hadamard product, such a density is defined in terms of the original matrices, as is common for many matrix-variate distributions, allowing matrix transformations to be handled in a natural way and then suitable statistical procedures to be developed.enghttp://www.sciencedirect.com/science/article/pii/S0047259X11001461Journal of Multivariate Analysis, febrero de 2012, volume 104, issue 1, pp 126-139ScopusConnection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributionsArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/access_right/c_16ecDepartamento de Ciencias Básicas, Universidad de Medellín, Medellín, ColombiaDepartamento de Estadística, Universidad de Valparaíso, Valparaíso, ChileDept. of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, CanadaKing Saud University, Faculty of Science, Riyadh, Saudi ArabiaCaro-Lopera F.J.Leiva V.Balakrishnan N.Generalized birnbaum-saunders distributionKronecker productMultivariate analysisSchur or entry-wise productShape theoryTHUMBNAILportada.JPGportada.JPGimage/jpeg15491http://repository.udem.edu.co/bitstream/11407/1363/1/portada.JPG6fa6a0a0325b5f3bcba2919e48722d05MD5111407/1363oai:repository.udem.edu.co:11407/13632020-05-27 17:30:53.916Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co
dc.title.eng.fl_str_mv Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions
title Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions
spellingShingle Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions
Generalized birnbaum-saunders distribution
Kronecker product
Multivariate analysis
Schur or entry-wise product
Shape theory
title_short Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions
title_full Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions
title_fullStr Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions
title_full_unstemmed Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions
title_sort Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions
dc.contributor.affiliation.spa.fl_str_mv Departamento de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia
Departamento de Estadística, Universidad de Valparaíso, Valparaíso, Chile
Dept. of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada
King Saud University, Faculty of Science, Riyadh, Saudi Arabia
dc.subject.keyword.eng.fl_str_mv Generalized birnbaum-saunders distribution
Kronecker product
Multivariate analysis
Schur or entry-wise product
Shape theory
topic Generalized birnbaum-saunders distribution
Kronecker product
Multivariate analysis
Schur or entry-wise product
Shape theory
description In this paper, we establish a connection between the Hadamard product and the usual matrix multiplication. In addition, we study some new properties of the Hadamard product and explore the inverse problem associated with the established connection, which facilitates diverse applications. Furthermore, we propose a matrix-variate generalized Birnbaum–Saunders (GBS) distribution. Three representations of the matrix-variate GBS density are provided, one of them by using the mentioned connection. The main motivation of this article is based on the fact that the representation of the matrix-variate GBS density based on element-by-element specification does not allow matrix transformations. Consequently, some statistical procedures based on this representation, such as multivariate data analysis and statistical shape theory, cannot be performed. For this reason, the primary goal of this work is to obtain a matrix representation of the matrix-variate GBS density that is useful for some statistical applications. When the GBS density is expressed by means of a matrix representation based on the Hadamard product, such a density is defined in terms of the original matrices, as is common for many matrix-variate distributions, allowing matrix transformations to be handled in a natural way and then suitable statistical procedures to be developed.
publishDate 2012
dc.date.created.none.fl_str_mv 2012
dc.date.accessioned.none.fl_str_mv 2015-10-09T13:17:52Z
dc.date.available.none.fl_str_mv 2015-10-09T13:17:52Z
dc.type.eng.fl_str_mv Article
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/article
dc.identifier.issn.none.fl_str_mv 0047259X
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/1363
dc.identifier.doi.none.fl_str_mv 10.1016/j.jmva.2011.07.004
identifier_str_mv 0047259X
10.1016/j.jmva.2011.07.004
url http://hdl.handle.net/11407/1363
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.isversionof.spa.fl_str_mv http://www.sciencedirect.com/science/article/pii/S0047259X11001461
dc.relation.ispartofen.eng.fl_str_mv Journal of Multivariate Analysis, febrero de 2012, volume 104, issue 1, pp 126-139
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dc.rights.accessrights.none.fl_str_mv info:eu-repo/semantics/restrictedAccess
eu_rights_str_mv restrictedAccess
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dc.source.spa.fl_str_mv Scopus
institution Universidad de Medellín
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repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
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