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Article: Practical higher-order smoothing of the bootstrap

TitlePractical higher-order smoothing of the bootstrap
Authors
KeywordsKernel function
Negativity correction
Rejection sampling
Sample quantile
Issue Date1994
PublisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/
Citation
Statistica Sinica, 1994, v. 4 n. 2, p. 445-459 How to Cite?
AbstractIn the context of functional estimation, the bootstrap approach amounts to substitution of the empirical distribution function for the unknown underlying distribution in the definition of the functional. A smoothed bootstrap alternative substitutes instead a smoothed version of the empirical distribution function, obtained by kernel smoothing of the given data sample. It may be theoretically advantageous to base such a smoothed bootstrap estimator on a higher-order kernel density estimator. Such density estimators necessarily take negative values, which creates a practical problem when simulation is to be used in construction of the bootstrap estimator. We illustrate how a negativity correction may be combined with rejection sampling to make higher-order smoothing feasible in the bootstrap context. Estimation of the variance of a sample quantile is examined both theoretically and in a simulation study.
Persistent Identifierhttp://hdl.handle.net/10722/53473
ISSN
2015 Impact Factor: 0.838
2015 SCImago Journal Rankings: 2.292

 

DC FieldValueLanguage
dc.contributor.authorLee, Sen_HK
dc.contributor.authorYoung, GAen_HK
dc.date.accessioned2009-04-03T07:20:50Z-
dc.date.available2009-04-03T07:20:50Z-
dc.date.issued1994en_HK
dc.identifier.citationStatistica Sinica, 1994, v. 4 n. 2, p. 445-459en_HK
dc.identifier.issn1017-0405en_HK
dc.identifier.urihttp://hdl.handle.net/10722/53473-
dc.description.abstractIn the context of functional estimation, the bootstrap approach amounts to substitution of the empirical distribution function for the unknown underlying distribution in the definition of the functional. A smoothed bootstrap alternative substitutes instead a smoothed version of the empirical distribution function, obtained by kernel smoothing of the given data sample. It may be theoretically advantageous to base such a smoothed bootstrap estimator on a higher-order kernel density estimator. Such density estimators necessarily take negative values, which creates a practical problem when simulation is to be used in construction of the bootstrap estimator. We illustrate how a negativity correction may be combined with rejection sampling to make higher-order smoothing feasible in the bootstrap context. Estimation of the variance of a sample quantile is examined both theoretically and in a simulation study.en_HK
dc.languageengen_HK
dc.publisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectKernel functionen_HK
dc.subjectNegativity correctionen_HK
dc.subjectRejection samplingen_HK
dc.subjectSample quantileen_HK
dc.titlePractical higher-order smoothing of the bootstrapen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1017-0405&volume=4&issue=2&spage=445&epage=459&date=1994&atitle=Practical+higher-order+smoothing+of+the+bootstrapen_HK
dc.identifier.emailLee, SMS: smslee@hkusua.hku.hken_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.hkuros4038-

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