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

Authors  
Keywords  M out of n bootstrap Quantile Smoothed bootstrap 
Issue Date  2005 
Publisher  Springer Verlag. 
Citation  Annals Of The Institute Of Statistical Mathematics, 2005, v. 57 n. 2, p. 279290 How to Cite? 
Abstract  We consider the problem of estimating the variance of a sample quantile calculated from a random sample of size n. The rthorder kernelsmoothed bootstrap estimator is known to yield an impressively small relative error of order O(nr/(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(n1/4), 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(n1/4) 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, simulationfree, 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 Identifier  http://hdl.handle.net/10722/82923 
ISSN  2015 Impact Factor: 0.768 2015 SCImago Journal Rankings: 0.931 
References 
DC Field  Value  Language 

dc.contributor.author  Cheung, KY  en_HK 
dc.contributor.author  Lee, SMS  en_HK 
dc.date.accessioned  20100906T08:34:56Z   
dc.date.available  20100906T08:34:56Z   
dc.date.issued  2005  en_HK 
dc.identifier.citation  Annals Of The Institute Of Statistical Mathematics, 2005, v. 57 n. 2, p. 279290  en_HK 
dc.identifier.issn  00203157  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/82923   
dc.description.abstract  We consider the problem of estimating the variance of a sample quantile calculated from a random sample of size n. The rthorder kernelsmoothed bootstrap estimator is known to yield an impressively small relative error of order O(nr/(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(n1/4), 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(n1/4) 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, simulationfree, 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.language  eng  en_HK 
dc.publisher  Springer Verlag.  en_HK 
dc.relation.ispartof  Annals of the Institute of Statistical Mathematics  en_HK 
dc.subject  M out of n bootstrap  en_HK 
dc.subject  Quantile  en_HK 
dc.subject  Smoothed bootstrap  en_HK 
dc.title  Variance estimation for sample quantiles using the m out of n bootstrap  en_HK 
dc.type  Article  en_HK 
dc.identifier.openurl  http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=00203157&volume=57&spage=279&epage=290&date=2005&atitle=Variance+estimation+for+sample+quantiles+using+the+m+out+of+n+bootstrap  en_HK 
dc.identifier.email  Lee, SMS: smslee@hku.hk  en_HK 
dc.identifier.authority  Lee, SMS=rp00726  en_HK 
dc.description.nature  link_to_subscribed_fulltext   
dc.identifier.scopus  eid_2s2.026244467939  en_HK 
dc.identifier.hkuros  100415  en_HK 
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.026244467939&selection=ref&src=s&origin=recordpage  en_HK 
dc.identifier.volume  57  en_HK 
dc.identifier.issue  2  en_HK 
dc.identifier.spage  279  en_HK 
dc.identifier.epage  290  en_HK 
dc.publisher.place  Germany  en_HK 
dc.identifier.scopusauthorid  Cheung, KY=35773070000  en_HK 
dc.identifier.scopusauthorid  Lee, SMS=24280225500  en_HK 