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Article: A recentred bootstrap procedure for constructing uniformly correct confidence sets under smooth function models

TitleA recentred bootstrap procedure for constructing uniformly correct confidence sets under smooth function models
Authors
KeywordsMoving-parameter
Recentred bootstrap
Smooth function model
Uniformly correct
Weighted bootstrap
Issue Date2017
PublisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/02331888.asp
Citation
Statistics, 2017, v. 51 n. 2, p. 277-293 How to Cite?
AbstractIt has been found, under a smooth function model setting, that the n out of n bootstrap is inconsistent at stationary points of the smooth function, but that the m out of n bootstrap is consistent, provided that a correct convergence rate is specified of the plug-in smooth function estimator. By considering a more general moving-parameter framework, we show that neither of the above bootstrap methods is consistent uniformly over neighbourhoods of stationary points, so that anomalies often arise of coverages of bootstrap sets over certain subsets of parameter values. We propose a recentred bootstrap procedure for constructing confidence sets with uniformly correct coverages over compact sets containing stationary points. A weighted bootstrap procedure is also proposed as an alternative under more general circumstances. Unlike the m out of n bootstrap, both procedures do not require knowledge of the convergence rate of the smooth function estimator. Empirical performance of our procedures is illustrated with numerical examples.
Persistent Identifierhttp://hdl.handle.net/10722/231325
ISSN
2017 Impact Factor: 0.606
2015 SCImago Journal Rankings: 0.664
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorYu, Z-
dc.contributor.authorLee, SMS-
dc.date.accessioned2016-09-20T05:22:19Z-
dc.date.available2016-09-20T05:22:19Z-
dc.date.issued2017-
dc.identifier.citationStatistics, 2017, v. 51 n. 2, p. 277-293-
dc.identifier.issn0233-1888-
dc.identifier.urihttp://hdl.handle.net/10722/231325-
dc.description.abstractIt has been found, under a smooth function model setting, that the n out of n bootstrap is inconsistent at stationary points of the smooth function, but that the m out of n bootstrap is consistent, provided that a correct convergence rate is specified of the plug-in smooth function estimator. By considering a more general moving-parameter framework, we show that neither of the above bootstrap methods is consistent uniformly over neighbourhoods of stationary points, so that anomalies often arise of coverages of bootstrap sets over certain subsets of parameter values. We propose a recentred bootstrap procedure for constructing confidence sets with uniformly correct coverages over compact sets containing stationary points. A weighted bootstrap procedure is also proposed as an alternative under more general circumstances. Unlike the m out of n bootstrap, both procedures do not require knowledge of the convergence rate of the smooth function estimator. Empirical performance of our procedures is illustrated with numerical examples.-
dc.languageeng-
dc.publisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/02331888.asp-
dc.relation.ispartofStatistics-
dc.rightsThis is an electronic version of an article published in Statistics. The article is available online at: http://dx.doi.org/10.1080/02331888.2016.1268612-
dc.subjectMoving-parameter-
dc.subjectRecentred bootstrap-
dc.subjectSmooth function model-
dc.subjectUniformly correct-
dc.subjectWeighted bootstrap-
dc.titleA recentred bootstrap procedure for constructing uniformly correct confidence sets under smooth function models-
dc.typeArticle-
dc.identifier.emailLee, SMS: smslee@hku.hk-
dc.identifier.authorityLee, SMS=rp00726-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1080/02331888.2016.1268612-
dc.identifier.scopuseid_2-s2.0-85006858093-
dc.identifier.hkuros266212-
dc.identifier.volume51-
dc.identifier.issue2-
dc.identifier.spage277-
dc.identifier.epage293-
dc.identifier.isiWOS:000394466300004-
dc.publisher.placeUnited Kingdom-

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