Concentration for high-dimensional linear processes with dependent innovations

Detalhes bibliográficos
Autor(a) principal: Leite, Fellipe Lopes Lima
Data de Publicação: 2023
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Institucional do FGV (FGV Repositório Digital)
Texto Completo: https://hdl.handle.net/10438/34642
Resumo: Nós desenvolvemos desigualdades de concentração para a norma l∞ de um vetor de processos lineares em sequências mixingale com caudas sub-Weibull. Essas desigualdades fazem uso da decomposição de Beveridge-Nelson, a qual reduz o problema para concentração da sup-norm de um vetor mixingale ou sua soma ponderada. Usando essa decomposição, nós desenvolvemos um limite de concentração para a norma de matrizes de auto-covariância de processos lineares. Esses resultados são úteis para estimação de limites para processos VAR de alta dimensão estimados usando regularização l1, bootstraps Gaussianos de alta dimensão para séries temporais e estimação de matrizes de covariância para processos longos.
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spelling Leite, Fellipe Lopes LimaEscolas::EMApCarvalho, Luiz Max FagundesFernandes, MarceloMendes, Eduardo Fonseca2023-12-19T17:03:46Z2023-12-19T17:03:46Z2023-03-21https://hdl.handle.net/10438/34642Nós desenvolvemos desigualdades de concentração para a norma l∞ de um vetor de processos lineares em sequências mixingale com caudas sub-Weibull. Essas desigualdades fazem uso da decomposição de Beveridge-Nelson, a qual reduz o problema para concentração da sup-norm de um vetor mixingale ou sua soma ponderada. Usando essa decomposição, nós desenvolvemos um limite de concentração para a norma de matrizes de auto-covariância de processos lineares. Esses resultados são úteis para estimação de limites para processos VAR de alta dimensão estimados usando regularização l1, bootstraps Gaussianos de alta dimensão para séries temporais e estimação de matrizes de covariância para processos longos.We develop concentration inequalities for l∞ norm of a vector linear processes on mixingale sequences with sub-Weibull tails. These inequalities make use of the Beveridge-Nelson decomposition, which reduces the problem to concentration for sup-norm of a vector-mixingale or its weighted sum. Using this decomposition, we derive a concentration bound for the maximum entrywise norm of auto-covariance matrices of linear processes. These results are useful for estimation bounds for high dimensional vector-autoregressive processes estimated using l1 regularization, high-dimensional Gaussian bootstrap for time-series, and long-run covariance matrix estimation.engProcessos GaussianosMatemática aplicadaMatrizes (Matemática)Processos gaussianosBootstrap (Estatística)Concentration for high-dimensional linear processes with dependent innovationsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional do FGV (FGV Repositório Digital)instname:Fundação Getulio Vargas (FGV)instacron:FGVinfo:eu-repo/semantics/openAccessORIGINALlplasso-dissertation-vFinal.pdflplasso-dissertation-vFinal.pdfapplication/pdf926431https://repositorio.fgv.br/bitstreams/7be29068-8844-41a0-9172-8c472aa0a877/download58c0e43419f3b91a7cb90e2b21f276d3MD51LICENSElicense.txtlicense.txttext/plain; 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dc.title.eng.fl_str_mv Concentration for high-dimensional linear processes with dependent innovations
title Concentration for high-dimensional linear processes with dependent innovations
spellingShingle Concentration for high-dimensional linear processes with dependent innovations
Leite, Fellipe Lopes Lima
Processos Gaussianos
Matemática aplicada
Matrizes (Matemática)
Processos gaussianos
Bootstrap (Estatística)
title_short Concentration for high-dimensional linear processes with dependent innovations
title_full Concentration for high-dimensional linear processes with dependent innovations
title_fullStr Concentration for high-dimensional linear processes with dependent innovations
title_full_unstemmed Concentration for high-dimensional linear processes with dependent innovations
title_sort Concentration for high-dimensional linear processes with dependent innovations
author Leite, Fellipe Lopes Lima
author_facet Leite, Fellipe Lopes Lima
author_role author
dc.contributor.unidadefgv.por.fl_str_mv Escolas::EMAp
dc.contributor.member.none.fl_str_mv Carvalho, Luiz Max Fagundes
Fernandes, Marcelo
dc.contributor.author.fl_str_mv Leite, Fellipe Lopes Lima
dc.contributor.advisor1.fl_str_mv Mendes, Eduardo Fonseca
contributor_str_mv Mendes, Eduardo Fonseca
dc.subject.por.fl_str_mv Processos Gaussianos
topic Processos Gaussianos
Matemática aplicada
Matrizes (Matemática)
Processos gaussianos
Bootstrap (Estatística)
dc.subject.bibliodata.por.fl_str_mv Matemática aplicada
Matrizes (Matemática)
Processos gaussianos
Bootstrap (Estatística)
description Nós desenvolvemos desigualdades de concentração para a norma l∞ de um vetor de processos lineares em sequências mixingale com caudas sub-Weibull. Essas desigualdades fazem uso da decomposição de Beveridge-Nelson, a qual reduz o problema para concentração da sup-norm de um vetor mixingale ou sua soma ponderada. Usando essa decomposição, nós desenvolvemos um limite de concentração para a norma de matrizes de auto-covariância de processos lineares. Esses resultados são úteis para estimação de limites para processos VAR de alta dimensão estimados usando regularização l1, bootstraps Gaussianos de alta dimensão para séries temporais e estimação de matrizes de covariância para processos longos.
publishDate 2023
dc.date.accessioned.fl_str_mv 2023-12-19T17:03:46Z
dc.date.available.fl_str_mv 2023-12-19T17:03:46Z
dc.date.issued.fl_str_mv 2023-03-21
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/10438/34642
url https://hdl.handle.net/10438/34642
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Institucional do FGV (FGV Repositório Digital)
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instacron:FGV
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institution FGV
reponame_str Repositório Institucional do FGV (FGV Repositório Digital)
collection Repositório Institucional do FGV (FGV Repositório Digital)
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