Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals
Autor(a) principal: | |
---|---|
Data de Publicação: | 2011 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/43977 https://doi.org/10.1007/s11009-011-9243-x |
Resumo: | Given a density $f$ we pose the problem of estimating the density functional $\psi_r=\int f^{(r)}f$ for a non-negative even $r$ making use of kernel methods. This is a well-known problem but some of its features remained unexplored. We focus on the problem of bandwidth selection. Whereas all the previous studies concentrate on an asymptotically optimal bandwidth here we study the properties of exact, non-asymptotic ones, and relate them with the former. Our main conclusion is that, despite being asymptotically equivalent, for realistic sample sizes much is lost by using the asymptotically optimal bandwidth. In contrast, as a target for data-driven selectors we propose another bandwidth which retains the small sample performance of the exact one. |
id |
RCAP_7ccfd7d41ff1d016f4f197dbdd75f6fe |
---|---|
oai_identifier_str |
oai:estudogeral.uc.pt:10316/43977 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density FunctionalsGiven a density $f$ we pose the problem of estimating the density functional $\psi_r=\int f^{(r)}f$ for a non-negative even $r$ making use of kernel methods. This is a well-known problem but some of its features remained unexplored. We focus on the problem of bandwidth selection. Whereas all the previous studies concentrate on an asymptotically optimal bandwidth here we study the properties of exact, non-asymptotic ones, and relate them with the former. Our main conclusion is that, despite being asymptotically equivalent, for realistic sample sizes much is lost by using the asymptotically optimal bandwidth. In contrast, as a target for data-driven selectors we propose another bandwidth which retains the small sample performance of the exact one.2011info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43977http://hdl.handle.net/10316/43977https://doi.org/10.1007/s11009-011-9243-xenghttps://link.springer.com/article/10.1007%2Fs11009-011-9243-xChacón, José E.Tenreiro, Carlosinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2021-06-29T10:02:54Zoai:estudogeral.uc.pt:10316/43977Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:30.688865Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals |
title |
Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals |
spellingShingle |
Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals Chacón, José E. |
title_short |
Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals |
title_full |
Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals |
title_fullStr |
Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals |
title_full_unstemmed |
Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals |
title_sort |
Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals |
author |
Chacón, José E. |
author_facet |
Chacón, José E. Tenreiro, Carlos |
author_role |
author |
author2 |
Tenreiro, Carlos |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Chacón, José E. Tenreiro, Carlos |
description |
Given a density $f$ we pose the problem of estimating the density functional $\psi_r=\int f^{(r)}f$ for a non-negative even $r$ making use of kernel methods. This is a well-known problem but some of its features remained unexplored. We focus on the problem of bandwidth selection. Whereas all the previous studies concentrate on an asymptotically optimal bandwidth here we study the properties of exact, non-asymptotic ones, and relate them with the former. Our main conclusion is that, despite being asymptotically equivalent, for realistic sample sizes much is lost by using the asymptotically optimal bandwidth. In contrast, as a target for data-driven selectors we propose another bandwidth which retains the small sample performance of the exact one. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/43977 http://hdl.handle.net/10316/43977 https://doi.org/10.1007/s11009-011-9243-x |
url |
http://hdl.handle.net/10316/43977 https://doi.org/10.1007/s11009-011-9243-x |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://link.springer.com/article/10.1007%2Fs11009-011-9243-x |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
_version_ |
1799133821631725568 |