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postgraduate thesis: Uniformly consistent bootstrap confidence intervals

TitleUniformly consistent bootstrap confidence intervals
Authors
Advisors
Advisor(s):Lee, SMS
Issue Date2012
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Yu, Z. [俞翥清]. (2012). Uniformly consistent bootstrap confidence intervals. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4775299
AbstractThe bootstrap methods are widely used for constructing confidence intervals. However, the conventional bootstrap fails to be consistent under some nonstandard circumstances. The m out of n bootstrap is usually adopted to restore consistency, provided that a correct convergence rate can be specified for the plug-in estimators. In this thesis, we re-investigate the asymptotic properties of the bootstrap in a moving-parameter framework in which the underlying distribution is allowed to depend on n. We consider the problem of setting uniformly consistent confidence intervals for two non-regular cases: (1) the smooth function models with vanishing derivatives; and (2) the M-estimation with non-regular conditions. Under the moving-parameter setup, neither the conventional bootstrap nor the m out of n bootstrap is shown uniformly consistent over the whole parameter space. The results reflect to some extent finite-sample anomalies that cannot be explained by conventional, fixed-parameter, asymptotics. We propose a weighted bootstrap procedure for constructing uniformly consistent bootstrap confidence intervals, which does not require explicit specification of the convergence rate of the plug-in estimator. Under the smooth function models, we also propose a modified n out of n bootstrap procedure in special cases where the smooth function is applied to estimators that are uniformly bootstrappable. The estimating function bootstrap is also successfully employed for the latter model and enjoys computational advantages over the weighted bootstrap. We illustrate our findings by comparing the finite-sample coverage performances of the different bootstrap procedures. The stable performance of the proposed methods, contrasts sharply with the erratic coverages of the n out of n and m out of n bootstrap intervals, a result in agreement with our theoretical findings.
DegreeMaster of Philosophy
SubjectBootstrap (Statistics)
Confidence intervals.
Dept/ProgramStatistics and Actuarial Science

 

DC FieldValueLanguage
dc.contributor.advisorLee, SMS-
dc.contributor.authorYu, Zhuqing.-
dc.contributor.author俞翥清.-
dc.date.issued2012-
dc.identifier.citationYu, Z. [俞翥清]. (2012). Uniformly consistent bootstrap confidence intervals. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4775299-
dc.description.abstractThe bootstrap methods are widely used for constructing confidence intervals. However, the conventional bootstrap fails to be consistent under some nonstandard circumstances. The m out of n bootstrap is usually adopted to restore consistency, provided that a correct convergence rate can be specified for the plug-in estimators. In this thesis, we re-investigate the asymptotic properties of the bootstrap in a moving-parameter framework in which the underlying distribution is allowed to depend on n. We consider the problem of setting uniformly consistent confidence intervals for two non-regular cases: (1) the smooth function models with vanishing derivatives; and (2) the M-estimation with non-regular conditions. Under the moving-parameter setup, neither the conventional bootstrap nor the m out of n bootstrap is shown uniformly consistent over the whole parameter space. The results reflect to some extent finite-sample anomalies that cannot be explained by conventional, fixed-parameter, asymptotics. We propose a weighted bootstrap procedure for constructing uniformly consistent bootstrap confidence intervals, which does not require explicit specification of the convergence rate of the plug-in estimator. Under the smooth function models, we also propose a modified n out of n bootstrap procedure in special cases where the smooth function is applied to estimators that are uniformly bootstrappable. The estimating function bootstrap is also successfully employed for the latter model and enjoys computational advantages over the weighted bootstrap. We illustrate our findings by comparing the finite-sample coverage performances of the different bootstrap procedures. The stable performance of the proposed methods, contrasts sharply with the erratic coverages of the n out of n and m out of n bootstrap intervals, a result in agreement with our 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/B47752993-
dc.subject.lcshBootstrap (Statistics)-
dc.subject.lcshConfidence intervals.-
dc.titleUniformly consistent bootstrap confidence intervals-
dc.typePG_Thesis-
dc.identifier.hkulb4775299-
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_b4775299-
dc.date.hkucongregation2012-

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