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postgraduate thesis: Hybrid bootstrap procedures for shrinkage-type estimators

TitleHybrid bootstrap procedures for shrinkage-type estimators
Authors
Advisors
Advisor(s):Lee, SMS
Issue Date2012
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Chan, T. [陳子軒]. (2012). Hybrid bootstrap procedures for shrinkage-type estimators. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4852182
AbstractIn statistical inference, one is often interested in estimating the distribution of a root, which is a function of the data and the parameters only. Knowledge of the distribution of a root is useful for inference problems such as hypothesis testing and the construction of a confidence set. Shrinkage-type estimators have become popular in statistical inference due to their smaller mean squared errors. In this thesis, the performance of different bootstrap methods is investigated for estimating the distributions of roots which are constructed based on shrinkage estimators. Focus is on two shrinkage estimation problems, namely the James-Stein estimation and the model selection problem in simple linear regression. A hybrid bootstrap procedure and a bootstrap test method are proposed to estimate the distributions of the roots of interest. In the two shrinkage problems, the asymptotic errors of the traditional n-out-of-n bootstrap, m-out-of-n bootstrap and the proposed methods are derived under a moving parameter framework. The problem of the lack of uniform consistency of the n-out-of-n and the m-out-of-n bootstraps is exposed. It is shown that the proposed methods have better overall performance, in the sense that they yield improved convergence rates over almost the whole range of possible values of the underlying parameters. Simulation studies are carried out to illustrate the theoretical findings.
DegreeMaster of Philosophy
SubjectBootstrap (Statistics)
Estimation theory.
Dept/ProgramStatistics and Actuarial Science

 

DC FieldValueLanguage
dc.contributor.advisorLee, SMS-
dc.contributor.authorChan, Tsz-hin.-
dc.contributor.author陳子軒.-
dc.date.issued2012-
dc.identifier.citationChan, T. [陳子軒]. (2012). Hybrid bootstrap procedures for shrinkage-type estimators. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4852182-
dc.description.abstractIn statistical inference, one is often interested in estimating the distribution of a root, which is a function of the data and the parameters only. Knowledge of the distribution of a root is useful for inference problems such as hypothesis testing and the construction of a confidence set. Shrinkage-type estimators have become popular in statistical inference due to their smaller mean squared errors. In this thesis, the performance of different bootstrap methods is investigated for estimating the distributions of roots which are constructed based on shrinkage estimators. Focus is on two shrinkage estimation problems, namely the James-Stein estimation and the model selection problem in simple linear regression. A hybrid bootstrap procedure and a bootstrap test method are proposed to estimate the distributions of the roots of interest. In the two shrinkage problems, the asymptotic errors of the traditional n-out-of-n bootstrap, m-out-of-n bootstrap and the proposed methods are derived under a moving parameter framework. The problem of the lack of uniform consistency of the n-out-of-n and the m-out-of-n bootstraps is exposed. It is shown that the proposed methods have better overall performance, in the sense that they yield improved convergence rates over almost the whole range of possible values of the underlying parameters. Simulation studies are carried out to illustrate the theoretical findings.-
dc.languageeng-
dc.publisherThe University of Hong Kong (Pokfulam, Hong Kong)-
dc.relation.ispartofHKU Theses Online (HKUTO)-
dc.rightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.source.urihttp://hub.hku.hk/bib/B48521826-
dc.subject.lcshBootstrap (Statistics)-
dc.subject.lcshEstimation theory.-
dc.titleHybrid bootstrap procedures for shrinkage-type estimators-
dc.typePG_Thesis-
dc.identifier.hkulb4852182-
dc.description.thesisnameMaster of Philosophy-
dc.description.thesislevelMaster-
dc.description.thesisdisciplineStatistics and Actuarial Science-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.5353/th_b4852182-
dc.date.hkucongregation2012-

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