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Article: Iterated smoothed bootstrap confidence intervals for population quantiles

TitleIterated smoothed bootstrap confidence intervals for population quantiles
Authors
KeywordsBandwidth
Bootstrap-t
Iterated bootstrap
Kernel
Quantile
Smoothed bootstrap
Studentized sample quantile
Issue Date2005
PublisherInstitute of Mathematical Statistics.
Citation
Annals Of Statistics, 2005, v. 33 n. 1, p. 437-462 How to Cite?
AbstractThis paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap-t confidence intervals for population quantiles, and establishes the optimal kernel band-widths at various stages of the smoothing procedures. The conventional smoothed bootstrap and bootstrap-t methods have been known to yield one-sided coverage errors of orders O(n -1/2) and o(n -2/3), respectively, for intervals based on the sample quantile of a random sample of size n. We sharpen the latter result to O (n -5/6) with proper choices of bandwidths at the bootstrapping and Studentization steps. We show further that calibration of the nominal coverage level by means of the iterated bootstrap succeeds in reducing the coverage error of the smoothed bootstrap percentile interval to the order O(n -2/3) and that of the smoothed bootstrap-t interval to O(n -58/57), provided that bandwidths are selected of appropriate orders. Simulation results confirm our asymptotic findings, suggesting that the iterated smoothed bootstrap-t method yields the most accurate coverage. On the other hand, the iterated smoothed bootstrap percentile method interval has the advantage of being shorter and more stable than the bootstrap-t intervals. © Institute of Mathematical Statistics, 2005.
Persistent Identifierhttp://hdl.handle.net/10722/43498
ISSN
2015 Impact Factor: 2.78
2015 SCImago Journal Rankings: 6.653
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorHo, YHSen_HK
dc.contributor.authorLee, SMSen_HK
dc.date.accessioned2007-03-23T04:47:13Z-
dc.date.available2007-03-23T04:47:13Z-
dc.date.issued2005en_HK
dc.identifier.citationAnnals Of Statistics, 2005, v. 33 n. 1, p. 437-462en_HK
dc.identifier.issn0090-5364en_HK
dc.identifier.urihttp://hdl.handle.net/10722/43498-
dc.description.abstractThis paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap-t confidence intervals for population quantiles, and establishes the optimal kernel band-widths at various stages of the smoothing procedures. The conventional smoothed bootstrap and bootstrap-t methods have been known to yield one-sided coverage errors of orders O(n -1/2) and o(n -2/3), respectively, for intervals based on the sample quantile of a random sample of size n. We sharpen the latter result to O (n -5/6) with proper choices of bandwidths at the bootstrapping and Studentization steps. We show further that calibration of the nominal coverage level by means of the iterated bootstrap succeeds in reducing the coverage error of the smoothed bootstrap percentile interval to the order O(n -2/3) and that of the smoothed bootstrap-t interval to O(n -58/57), provided that bandwidths are selected of appropriate orders. Simulation results confirm our asymptotic findings, suggesting that the iterated smoothed bootstrap-t method yields the most accurate coverage. On the other hand, the iterated smoothed bootstrap percentile method interval has the advantage of being shorter and more stable than the bootstrap-t intervals. © Institute of Mathematical Statistics, 2005.en_HK
dc.format.extent1201189 bytes-
dc.format.extent26112 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/msword-
dc.languageengen_HK
dc.publisherInstitute of Mathematical Statistics.en_HK
dc.relation.ispartofAnnals of Statisticsen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectBandwidthen_HK
dc.subjectBootstrap-ten_HK
dc.subjectIterated bootstrapen_HK
dc.subjectKernelen_HK
dc.subjectQuantileen_HK
dc.subjectSmoothed bootstrapen_HK
dc.subjectStudentized sample quantileen_HK
dc.titleIterated smoothed bootstrap confidence intervals for population quantilesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0090-5364&volume=33&issue=1&spage=437&epage=462&date=2005&atitle=Iterated+smoothed+bootstrap+confidence+intervals+for+population+quantilesen_HK
dc.identifier.emailLee, SMS: smslee@hku.hken_HK
dc.identifier.authorityLee, SMS=rp00726en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1214/009053604000000878en_HK
dc.identifier.scopuseid_2-s2.0-15844389605en_HK
dc.identifier.hkuros100410-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-15844389605&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume33en_HK
dc.identifier.issue1en_HK
dc.identifier.spage437en_HK
dc.identifier.epage462en_HK
dc.identifier.isiWOS:000228576800020-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridHo, YHS=8378552000en_HK
dc.identifier.scopusauthoridLee, SMS=24280225500en_HK

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