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Article: Variance estimation for sample quantiles using the m out of n bootstrap

TitleVariance estimation for sample quantiles using the m out of n bootstrap
Authors
KeywordsM out of n bootstrap
Quantile
Smoothed bootstrap
Issue Date2005
PublisherSpringer Verlag.
Citation
Annals Of The Institute Of Statistical Mathematics, 2005, v. 57 n. 2, p. 279-290 How to Cite?
AbstractWe consider the problem of estimating the variance of a sample quantile calculated from a random sample of size n. The r-th-order kernel-smoothed bootstrap estimator is known to yield an impressively small relative error of order O(n-r/(2r+1)). It nevertheless requires strong smoothness conditions on the underlying density function, and has a performance very sensitive to the precise choice of the bandwidth. The unsmoothed bootstrap has a poorer relative error of order O(n-1/4), but works for less smooth density functions. We investigate a modified form of the bootstrap, known as the m out of n bootstrap, and show that it yields a relative error of order smaller than O(n-1/4) under the same smoothness conditions required by the conventional unsmoothed bootstrap on the density function, provided that the bootstrap sample size m is of an appropriate order. The estimator permits exact, simulation-free, computation and has accuracy fairly insensitive to the precise choice of m. A simulation study is reported to provide empirical comparison of the various methods. © 2005 The Institute of Statistical Mathematics.
Persistent Identifierhttp://hdl.handle.net/10722/82923
ISSN
2015 Impact Factor: 0.768
2015 SCImago Journal Rankings: 0.931
References

 

DC FieldValueLanguage
dc.contributor.authorCheung, KYen_HK
dc.contributor.authorLee, SMSen_HK
dc.date.accessioned2010-09-06T08:34:56Z-
dc.date.available2010-09-06T08:34:56Z-
dc.date.issued2005en_HK
dc.identifier.citationAnnals Of The Institute Of Statistical Mathematics, 2005, v. 57 n. 2, p. 279-290en_HK
dc.identifier.issn0020-3157en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82923-
dc.description.abstractWe consider the problem of estimating the variance of a sample quantile calculated from a random sample of size n. The r-th-order kernel-smoothed bootstrap estimator is known to yield an impressively small relative error of order O(n-r/(2r+1)). It nevertheless requires strong smoothness conditions on the underlying density function, and has a performance very sensitive to the precise choice of the bandwidth. The unsmoothed bootstrap has a poorer relative error of order O(n-1/4), but works for less smooth density functions. We investigate a modified form of the bootstrap, known as the m out of n bootstrap, and show that it yields a relative error of order smaller than O(n-1/4) under the same smoothness conditions required by the conventional unsmoothed bootstrap on the density function, provided that the bootstrap sample size m is of an appropriate order. The estimator permits exact, simulation-free, computation and has accuracy fairly insensitive to the precise choice of m. A simulation study is reported to provide empirical comparison of the various methods. © 2005 The Institute of Statistical Mathematics.en_HK
dc.languageengen_HK
dc.publisherSpringer Verlag.en_HK
dc.relation.ispartofAnnals of the Institute of Statistical Mathematicsen_HK
dc.subjectM out of n bootstrapen_HK
dc.subjectQuantileen_HK
dc.subjectSmoothed bootstrapen_HK
dc.titleVariance estimation for sample quantiles using the m out of n bootstrapen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0020-3157&volume=57&spage=279&epage=290&date=2005&atitle=Variance+estimation+for+sample+quantiles+using+the+m+out+of+n+bootstrapen_HK
dc.identifier.emailLee, SMS: smslee@hku.hken_HK
dc.identifier.authorityLee, SMS=rp00726en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-26244467939en_HK
dc.identifier.hkuros100415en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-26244467939&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume57en_HK
dc.identifier.issue2en_HK
dc.identifier.spage279en_HK
dc.identifier.epage290en_HK
dc.publisher.placeGermanyen_HK
dc.identifier.scopusauthoridCheung, KY=35773070000en_HK
dc.identifier.scopusauthoridLee, SMS=24280225500en_HK

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