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Article: Stein confidence sets based on non-iterated and iterated parametric bootstraps

TitleStein confidence sets based on non-iterated and iterated parametric bootstraps
Authors
KeywordsConfidence set
Consistency
Coverage error
Iterated bootstrap
m out of n parametric bootstrap
Minimax
Stein estimator
Issue Date2006
PublisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/
Citation
Statistica Sinica, 2006, v. 16 n. 1, p. 45-75 How to Cite?
AbstractFor estimation of a d-variate mean vector 6 based on a random sample of size n drawn from a distribution of a location family, a generalized Stein estimator T n,S may be defined which shrinks the sample mean towards a proper linear subspace double-struck L sign of ℝ d. In general, the conventional parametric bootstrap consistently estimates the limit distribution of n 1/2 (T n,S - θ) when θ ∉ double-struck L sign but fails to be consistent otherwise. We establish consistency of two modified forms of the parametric bootstrap for any θ ∈ ℝ d, which are therefore useful for statistical inference about 9. In the context of constructing confidence sets for θ, we show that the first approach, which is based on the m out of n bootstrap, yields coverage error of order O(n -1/4) for all θ, provided that the bootstrap resample size m has an order determined by a minimax criterion. The second approach bootstraps from a distribution with an adaptively estimated mean vector, and is shown to yield coverage error of exponentially small order for θ ∈ double-struck L sign and of order O(n -1) for θ ∉ double-struck L sign. Iterated versions of the two approaches are also developed to give improved orders of coverage error. A simulation study is reported to illustrate our asymptotic findings.
Persistent Identifierhttp://hdl.handle.net/10722/44877
ISSN
2015 Impact Factor: 0.838
2015 SCImago Journal Rankings: 2.292
References

 

DC FieldValueLanguage
dc.contributor.authorCheung, KYen_HK
dc.contributor.authorLee, SMSen_HK
dc.contributor.authorYoung, GAen_HK
dc.date.accessioned2007-10-30T06:12:22Z-
dc.date.available2007-10-30T06:12:22Z-
dc.date.issued2006en_HK
dc.identifier.citationStatistica Sinica, 2006, v. 16 n. 1, p. 45-75en_HK
dc.identifier.issn1017-0405en_HK
dc.identifier.urihttp://hdl.handle.net/10722/44877-
dc.description.abstractFor estimation of a d-variate mean vector 6 based on a random sample of size n drawn from a distribution of a location family, a generalized Stein estimator T n,S may be defined which shrinks the sample mean towards a proper linear subspace double-struck L sign of ℝ d. In general, the conventional parametric bootstrap consistently estimates the limit distribution of n 1/2 (T n,S - θ) when θ ∉ double-struck L sign but fails to be consistent otherwise. We establish consistency of two modified forms of the parametric bootstrap for any θ ∈ ℝ d, which are therefore useful for statistical inference about 9. In the context of constructing confidence sets for θ, we show that the first approach, which is based on the m out of n bootstrap, yields coverage error of order O(n -1/4) for all θ, provided that the bootstrap resample size m has an order determined by a minimax criterion. The second approach bootstraps from a distribution with an adaptively estimated mean vector, and is shown to yield coverage error of exponentially small order for θ ∈ double-struck L sign and of order O(n -1) for θ ∉ double-struck L sign. Iterated versions of the two approaches are also developed to give improved orders of coverage error. A simulation study is reported to illustrate our asymptotic findings.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.relation.ispartofStatistica Sinicaen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectConfidence seten_HK
dc.subjectConsistencyen_HK
dc.subjectCoverage erroren_HK
dc.subjectIterated bootstrapen_HK
dc.subjectm out of n parametric bootstrapen_HK
dc.subjectMinimaxen_HK
dc.subjectStein estimatoren_HK
dc.titleStein confidence sets based on non-iterated and iterated parametric bootstrapsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1017-0405&volume=16&issue=1&spage=45&epage=75&date=2006&atitle=Stein+confidence+sets+based+on+non-iterated+and+iterated+parametric+bootstrapsen_HK
dc.identifier.emailLee, SMS: smslee@hku.hken_HK
dc.identifier.authorityLee, SMS=rp00726en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.scopuseid_2-s2.0-33646397043en_HK
dc.identifier.hkuros115380-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33646397043&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume16en_HK
dc.identifier.issue1en_HK
dc.identifier.spage45en_HK
dc.identifier.epage75en_HK
dc.publisher.placeTaiwan, Republic of Chinaen_HK
dc.identifier.scopusauthoridCheung, KY=35773070000en_HK
dc.identifier.scopusauthoridLee, SMS=24280225500en_HK
dc.identifier.scopusauthoridYoung, GA=36723800600en_HK

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