Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning

Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges more slowly than at the canonical rate of $\mathcal{O}(1/n)...

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Detalles Bibliográficos
Autores: L'Ecuyer, P., Puchhammer, F., Ben Abdellah, A.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1327
Acceso en línea:http://hdl.handle.net/20.500.11824/1327
Access Level:acceso abierto
Palabra clave:density estimation
conditional Monte Carlo
quasi-Monte Carlo
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spelling Monte Carlo and Quasi-Monte Carlo Density Estimation via ConditioningL'Ecuyer, P.Puchhammer, F.Ben Abdellah, A.density estimationconditional Monte Carloquasi-Monte CarloEstimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges more slowly than at the canonical rate of $\mathcal{O}(1/n)$. When the sample is generated from a simulation model and we have control over how this is done, we can do better. We examine an approach in which conditional Monte Carlo yields, under certain conditions, a random conditional density which is an unbiased estimator of the true density at any point. By averaging independent replications, we obtain a density estimator that converges at a faster rate than the usual ones. Moreover, combining this new type of estimator with randomized quasi-Monte Carlo to generate the samples typically brings a larger improvement on the error and convergence rate than for the usual estimators, because the new estimator is smoother as a function of the underlying uniform random numbers.IVADO Research Grant, NSERC-Canada Discorvery Grant, Canada Research Chair, Inria International Chair, ERDF, ESF, EXP. 2019/00432202120212021info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1327reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Inglésinfo:eu-repo/grantAgreement/MINECO//SEV-2017-0718info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104927GB-C22info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108111RB-I00info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021info:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEK/Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/13272026-06-19T12:47:47Z
dc.title.none.fl_str_mv Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning
title Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning
spellingShingle Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning
L'Ecuyer, P.
density estimation
conditional Monte Carlo
quasi-Monte Carlo
title_short Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning
title_full Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning
title_fullStr Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning
title_full_unstemmed Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning
title_sort Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning
dc.creator.none.fl_str_mv L'Ecuyer, P.
Puchhammer, F.
Ben Abdellah, A.
author L'Ecuyer, P.
author_facet L'Ecuyer, P.
Puchhammer, F.
Ben Abdellah, A.
author_role author
author2 Puchhammer, F.
Ben Abdellah, A.
author2_role author
author
dc.subject.none.fl_str_mv density estimation
conditional Monte Carlo
quasi-Monte Carlo
topic density estimation
conditional Monte Carlo
quasi-Monte Carlo
description Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges more slowly than at the canonical rate of $\mathcal{O}(1/n)$. When the sample is generated from a simulation model and we have control over how this is done, we can do better. We examine an approach in which conditional Monte Carlo yields, under certain conditions, a random conditional density which is an unbiased estimator of the true density at any point. By averaging independent replications, we obtain a density estimator that converges at a faster rate than the usual ones. Moreover, combining this new type of estimator with randomized quasi-Monte Carlo to generate the samples typically brings a larger improvement on the error and convergence rate than for the usual estimators, because the new estimator is smoother as a function of the underlying uniform random numbers.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021
2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1327
url http://hdl.handle.net/20.500.11824/1327
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104927GB-C22
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108111RB-I00
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
info:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEK/
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
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