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Article: Stein confidence sets based on non-iterated and iterated parametric bootstraps
Title | Stein confidence sets based on non-iterated and iterated parametric bootstraps |
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Authors | |
Keywords | Confidence set Consistency Coverage error Iterated bootstrap m out of n parametric bootstrap Minimax Stein estimator |
Issue Date | 2006 |
Publisher | Academia 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? |
Abstract | For 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 Identifier | http://hdl.handle.net/10722/44877 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 1.368 |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Cheung, KY | en_HK |
dc.contributor.author | Lee, SMS | en_HK |
dc.contributor.author | Young, GA | en_HK |
dc.date.accessioned | 2007-10-30T06:12:22Z | - |
dc.date.available | 2007-10-30T06:12:22Z | - |
dc.date.issued | 2006 | en_HK |
dc.identifier.citation | Statistica Sinica, 2006, v. 16 n. 1, p. 45-75 | en_HK |
dc.identifier.issn | 1017-0405 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/44877 | - |
dc.description.abstract | For 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.language | eng | en_HK |
dc.publisher | Academia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/ | en_HK |
dc.relation.ispartof | Statistica Sinica | en_HK |
dc.subject | Confidence set | en_HK |
dc.subject | Consistency | en_HK |
dc.subject | Coverage error | en_HK |
dc.subject | Iterated bootstrap | en_HK |
dc.subject | m out of n parametric bootstrap | en_HK |
dc.subject | Minimax | en_HK |
dc.subject | Stein estimator | en_HK |
dc.title | Stein confidence sets based on non-iterated and iterated parametric bootstraps | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+bootstraps | en_HK |
dc.identifier.email | Lee, SMS: smslee@hku.hk | en_HK |
dc.identifier.authority | Lee, SMS=rp00726 | en_HK |
dc.description.nature | published_or_final_version | en_HK |
dc.identifier.scopus | eid_2-s2.0-33646397043 | en_HK |
dc.identifier.hkuros | 115380 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-33646397043&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 16 | en_HK |
dc.identifier.issue | 1 | en_HK |
dc.identifier.spage | 45 | en_HK |
dc.identifier.epage | 75 | en_HK |
dc.publisher.place | Taiwan, Republic of China | en_HK |
dc.identifier.scopusauthorid | Cheung, KY=35773070000 | en_HK |
dc.identifier.scopusauthorid | Lee, SMS=24280225500 | en_HK |
dc.identifier.scopusauthorid | Young, GA=36723800600 | en_HK |
dc.identifier.issnl | 1017-0405 | - |