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Article: Iterated bootstrap-t confidence intervals for density functions

TitleIterated bootstrap-t confidence intervals for density functions
Authors
KeywordsBias
Bootstrap-t
Density function
Iterated bootstrap
Kernel density estimate
Undersmoothing
Issue Date2008
PublisherBlackwell Publishing Ltd. The Journal's web site is located at http://www.blackwellpublishing.com/journals/SJOS
Citation
Scandinavian Journal Of Statistics, 2008, v. 35 n. 2, p. 295-308 How to Cite?
AbstractConventional bootstrap-t intervals for density functions based on kernel density estimators exhibit poor coverages due to failure of the bootstrap to estimate the bias correctly. The problem can be resolved by either estimating the bias explicitly or undersmoothing the kernel density estimate to undermine its bias asymptotically. The resulting bias-corrected intervals have an optimal coverage error of order arbitrarily close to second order for a sufficiently smooth density function. We investigated the effects on coverage error of both bias-corrected intervals when the nominal coverage level is calibrated by the iterated bootstrap. In either case, an asymptotic reduction of coverage error is possible provided that the bias terms are handled using an extra round of smoothed bootstrapping. Under appropriate smoothness conditions, the optimal coverage error of the iterated bootstrap-t intervals has order arbitrarily close to third order. Examples of both simulated and real data are reported to illustrate the iterated bootstrap procedures. © 2007 Board of the Foundation of the Scandinavian Journal of Statistics.
Persistent Identifierhttp://hdl.handle.net/10722/83061
ISSN
2015 Impact Factor: 0.908
2015 SCImago Journal Rankings: 1.362
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHo, YHSen_HK
dc.contributor.authorLee, SMSen_HK
dc.date.accessioned2010-09-06T08:36:28Z-
dc.date.available2010-09-06T08:36:28Z-
dc.date.issued2008en_HK
dc.identifier.citationScandinavian Journal Of Statistics, 2008, v. 35 n. 2, p. 295-308en_HK
dc.identifier.issn0303-6898en_HK
dc.identifier.urihttp://hdl.handle.net/10722/83061-
dc.description.abstractConventional bootstrap-t intervals for density functions based on kernel density estimators exhibit poor coverages due to failure of the bootstrap to estimate the bias correctly. The problem can be resolved by either estimating the bias explicitly or undersmoothing the kernel density estimate to undermine its bias asymptotically. The resulting bias-corrected intervals have an optimal coverage error of order arbitrarily close to second order for a sufficiently smooth density function. We investigated the effects on coverage error of both bias-corrected intervals when the nominal coverage level is calibrated by the iterated bootstrap. In either case, an asymptotic reduction of coverage error is possible provided that the bias terms are handled using an extra round of smoothed bootstrapping. Under appropriate smoothness conditions, the optimal coverage error of the iterated bootstrap-t intervals has order arbitrarily close to third order. Examples of both simulated and real data are reported to illustrate the iterated bootstrap procedures. © 2007 Board of the Foundation of the Scandinavian Journal of Statistics.en_HK
dc.languageengen_HK
dc.publisherBlackwell Publishing Ltd. The Journal's web site is located at http://www.blackwellpublishing.com/journals/SJOSen_HK
dc.relation.ispartofScandinavian Journal of Statisticsen_HK
dc.rightsScandinavian Journal of Statistics. Copyright © Blackwell Publishing Ltd.en_HK
dc.subjectBiasen_HK
dc.subjectBootstrap-ten_HK
dc.subjectDensity functionen_HK
dc.subjectIterated bootstrapen_HK
dc.subjectKernel density estimateen_HK
dc.subjectUndersmoothingen_HK
dc.titleIterated bootstrap-t confidence intervals for density functionsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0303-6898&volume=35&spage=295&epage=308&date=2008&atitle=Iterated+bootstrap-t+confidence+intervals+for+density+functionsen_HK
dc.identifier.emailLee, SMS: smslee@hku.hken_HK
dc.identifier.authorityLee, SMS=rp00726en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1111/j.1467-9469.2007.00577.xen_HK
dc.identifier.scopuseid_2-s2.0-43749096354en_HK
dc.identifier.hkuros150492en_HK
dc.identifier.volume35en_HK
dc.identifier.issue2en_HK
dc.identifier.spage295en_HK
dc.identifier.epage308en_HK
dc.identifier.isiWOS:000255836500007-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridHo, YHS=8378552000en_HK
dc.identifier.scopusauthoridLee, SMS=24280225500en_HK
dc.identifier.citeulike2803024-

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