Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models

Autores
Bura, Efstathia; Duarte, S.; Forzani, Liliana Maria; Smucler, Ezequiel; Sued, Raquel Mariela
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates.
Fil: Bura, Efstathia. The George Washington University; Estados Unidos. Vienna University of Technology; Austria
Fil: Duarte, S.. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Smucler, Ezequiel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Sued, Raquel Mariela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
EXPONENTIAL FAMILY
M-ESTIMATION
NON-CONVEX
PARAMETER SPACES
RANK RESTRICTION
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:11336/162204
Acceder
id CONICETDig_0973486a16410206ae55f87bb0391c6a
oai_identifier_str oai:ri.conicet.gov.ar:11336/162204
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear modelsBura, EfstathiaDuarte, S.Forzani, Liliana MariaSmucler, EzequielSued, Raquel MarielaEXPONENTIAL FAMILYM-ESTIMATIONNON-CONVEXPARAMETER SPACESRANK RESTRICTIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates.Fil: Bura, Efstathia. The George Washington University; Estados Unidos. Vienna University of Technology; AustriaFil: Duarte, S.. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaFil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaFil: Smucler, Ezequiel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Sued, Raquel Mariela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaTaylor & Francis Ltd2018-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/162204Bura, Efstathia; Duarte, S.; Forzani, Liliana Maria; Smucler, Ezequiel; Sued, Raquel Mariela; Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models; Taylor & Francis Ltd; Statistics; 52; 5; 9-2018; 1005-10240233-1888CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/full/10.1080/02331888.2018.1467420info:eu-repo/semantics/altIdentifier/doi/10.1080/02331888.2018.1467420info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T11:42:12Zoai:ri.conicet.gov.ar:11336/162204instacron: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:34982025-10-29 11:42:13.189CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models
title Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models
spellingShingle Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models
Bura, Efstathia
EXPONENTIAL FAMILY
M-ESTIMATION
NON-CONVEX
PARAMETER SPACES
RANK RESTRICTION
title_short Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models
title_full Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models
title_fullStr Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models
title_full_unstemmed Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models
title_sort Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models
dc.creator.none.fl_str_mv Bura, Efstathia
Duarte, S.
Forzani, Liliana Maria
Smucler, Ezequiel
Sued, Raquel Mariela
author Bura, Efstathia
author_facet Bura, Efstathia
Duarte, S.
Forzani, Liliana Maria
Smucler, Ezequiel
Sued, Raquel Mariela
author_role author
author2 Duarte, S.
Forzani, Liliana Maria
Smucler, Ezequiel
Sued, Raquel Mariela
author2_role author
author
author
author
dc.subject.none.fl_str_mv EXPONENTIAL FAMILY
M-ESTIMATION
NON-CONVEX
PARAMETER SPACES
RANK RESTRICTION
topic EXPONENTIAL FAMILY
M-ESTIMATION
NON-CONVEX
PARAMETER SPACES
RANK RESTRICTION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates.
Fil: Bura, Efstathia. The George Washington University; Estados Unidos. Vienna University of Technology; Austria
Fil: Duarte, S.. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Smucler, Ezequiel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Sued, Raquel Mariela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates.
publishDate 2018
dc.date.none.fl_str_mv 2018-09
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/11336/162204
Bura, Efstathia; Duarte, S.; Forzani, Liliana Maria; Smucler, Ezequiel; Sued, Raquel Mariela; Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models; Taylor & Francis Ltd; Statistics; 52; 5; 9-2018; 1005-1024
0233-1888
CONICET Digital
CONICET
url http://hdl.handle.net/11336/162204
identifier_str_mv Bura, Efstathia; Duarte, S.; Forzani, Liliana Maria; Smucler, Ezequiel; Sued, Raquel Mariela; Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models; Taylor & Francis Ltd; Statistics; 52; 5; 9-2018; 1005-1024
0233-1888
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/full/10.1080/02331888.2018.1467420
info:eu-repo/semantics/altIdentifier/doi/10.1080/02331888.2018.1467420
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis Ltd
publisher.none.fl_str_mv Taylor & Francis Ltd
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
_version_ 1847426333229973504
score 13.10058

Publicaciones similares