Global optimization of the CUE objective function by eigenvalue methods

Detalhes bibliográficos
Autor(a) principal: Exel, Guilherme Sohnlein
Data de Publicação: 2024
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Institucional do FGV (FGV Repositório Digital)
Texto Completo: https://hdl.handle.net/10438/35834
Resumo: Desde sua concepção em Hansen et al. (1996), o Estimador de GMM de Atualização Contínua (CUE) tem representado um desafio para os métodos de otimização numérica devido à estrutura de sua função objetivo. Mesmo em modelos lineares simples, ela pode apresentar múltiplos mínimos locais e seções planas que frequentemente derrotam tanto os métodos de descida de gradiente quanto os de busca em grade. Esse problema de longa data na literatura foi recentemente resolvido por Moreira et al. (2023). Construindo sobre este resultado, propomos um método alternativo que é simples de implementar e mantém garantias semelhantes de produzir resultados globalmente ótimos. Mostramos como as condições de primeira ordem da função objetivo do CUE podem ser reformuladas na forma de um problema de autovalores e especializadas para casos em que algoritmos eficientes estão disponíveis.
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spelling Exel, Guilherme SohnleinEscolas::EPGENewey, Whitney KentSant'Anna, Marcelo Castello BrancoSharifvaghefi, MahradMoreira, Marcelo J2024-09-03T17:51:21Z2024-09-03T17:51:21Z2024-03-26https://hdl.handle.net/10438/35834Desde sua concepção em Hansen et al. (1996), o Estimador de GMM de Atualização Contínua (CUE) tem representado um desafio para os métodos de otimização numérica devido à estrutura de sua função objetivo. Mesmo em modelos lineares simples, ela pode apresentar múltiplos mínimos locais e seções planas que frequentemente derrotam tanto os métodos de descida de gradiente quanto os de busca em grade. Esse problema de longa data na literatura foi recentemente resolvido por Moreira et al. (2023). Construindo sobre este resultado, propomos um método alternativo que é simples de implementar e mantém garantias semelhantes de produzir resultados globalmente ótimos. Mostramos como as condições de primeira ordem da função objetivo do CUE podem ser reformuladas na forma de um problema de autovalores e especializadas para casos em que algoritmos eficientes estão disponíveis.Since its inception in Hansen et al. (1996, the Continuously Updating GMM Estimator (CUE) has posed a challenge for numerical optimization methods due to the structure of its criterion function. Even in simple linear models, it can present multiple local minima and flat sections which often defeat both gradient descent and grid search methods. This longstanding problem in the literature has recently been solved by Moreira et al. (2023). We build upon their insight and propose an alternative method which is simple to implement and retains similar guarantees of producing globally optimal results. We show how the first order conditions of the CUE criterion function can be restated in the form of an eigenvalue problem and specialize to cases for which efficient algorithms are available.engEstimador de atualização contínuaMétodo generalizado dos momentosProblemas de autovalores não linearesProblemas de autovalores multiparamétricosContinuously updating estimatorGeneralized method of momentsNonlinear eigenvalue problemsMultiparameter eigenvalue problemsEconomiaEconometria – Processamento de dadosAutovaloresMetodo dos momentos (Estatistica)Otimização matemáticaGlobal optimization of the CUE objective function by eigenvalue methodsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional do FGV (FGV Repositório Digital)instname:Fundação Getulio Vargas 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dc.title.eng.fl_str_mv Global optimization of the CUE objective function by eigenvalue methods
title Global optimization of the CUE objective function by eigenvalue methods
spellingShingle Global optimization of the CUE objective function by eigenvalue methods
Exel, Guilherme Sohnlein
Estimador de atualização contínua
Método generalizado dos momentos
Problemas de autovalores não lineares
Problemas de autovalores multiparamétricos
Continuously updating estimator
Generalized method of moments
Nonlinear eigenvalue problems
Multiparameter eigenvalue problems
Economia
Econometria – Processamento de dados
Autovalores
Metodo dos momentos (Estatistica)
Otimização matemática
title_short Global optimization of the CUE objective function by eigenvalue methods
title_full Global optimization of the CUE objective function by eigenvalue methods
title_fullStr Global optimization of the CUE objective function by eigenvalue methods
title_full_unstemmed Global optimization of the CUE objective function by eigenvalue methods
title_sort Global optimization of the CUE objective function by eigenvalue methods
author Exel, Guilherme Sohnlein
author_facet Exel, Guilherme Sohnlein
author_role author
dc.contributor.unidadefgv.por.fl_str_mv Escolas::EPGE
dc.contributor.member.none.fl_str_mv Newey, Whitney Kent
Sant'Anna, Marcelo Castello Branco
Sharifvaghefi, Mahrad
dc.contributor.author.fl_str_mv Exel, Guilherme Sohnlein
dc.contributor.advisor1.fl_str_mv Moreira, Marcelo J
contributor_str_mv Moreira, Marcelo J
dc.subject.por.fl_str_mv Estimador de atualização contínua
topic Estimador de atualização contínua
Método generalizado dos momentos
Problemas de autovalores não lineares
Problemas de autovalores multiparamétricos
Continuously updating estimator
Generalized method of moments
Nonlinear eigenvalue problems
Multiparameter eigenvalue problems
Economia
Econometria – Processamento de dados
Autovalores
Metodo dos momentos (Estatistica)
Otimização matemática
dc.subject. por.fl_str_mv Método generalizado dos momentos
Problemas de autovalores não lineares
Problemas de autovalores multiparamétricos
dc.subject.eng.fl_str_mv Continuously updating estimator
Generalized method of moments
Nonlinear eigenvalue problems
Multiparameter eigenvalue problems
dc.subject.area.por.fl_str_mv Economia
dc.subject.bibliodata.por.fl_str_mv Econometria – Processamento de dados
Autovalores
Metodo dos momentos (Estatistica)
Otimização matemática
description Desde sua concepção em Hansen et al. (1996), o Estimador de GMM de Atualização Contínua (CUE) tem representado um desafio para os métodos de otimização numérica devido à estrutura de sua função objetivo. Mesmo em modelos lineares simples, ela pode apresentar múltiplos mínimos locais e seções planas que frequentemente derrotam tanto os métodos de descida de gradiente quanto os de busca em grade. Esse problema de longa data na literatura foi recentemente resolvido por Moreira et al. (2023). Construindo sobre este resultado, propomos um método alternativo que é simples de implementar e mantém garantias semelhantes de produzir resultados globalmente ótimos. Mostramos como as condições de primeira ordem da função objetivo do CUE podem ser reformuladas na forma de um problema de autovalores e especializadas para casos em que algoritmos eficientes estão disponíveis.
publishDate 2024
dc.date.accessioned.fl_str_mv 2024-09-03T17:51:21Z
dc.date.available.fl_str_mv 2024-09-03T17:51:21Z
dc.date.issued.fl_str_mv 2024-03-26
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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dc.identifier.uri.fl_str_mv https://hdl.handle.net/10438/35834
url https://hdl.handle.net/10438/35834
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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collection Repositório Institucional do FGV (FGV Repositório Digital)
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MD5
repository.name.fl_str_mv Repositório Institucional do FGV (FGV Repositório Digital) - Fundação Getulio Vargas (FGV)
repository.mail.fl_str_mv
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