The 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. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy
| Identifer | oai:union.ndltd.org:HKU/oai:hub.hku.hk:10722/174479 |
| Date | January 2012 |
| Creators | Yu, Zhuqing., 俞翥清. |
| Contributors | Lee, SMS |
| Publisher | The University of Hong Kong (Pokfulam, Hong Kong) |
| Source Sets | Hong Kong University Theses |
| Language | English |
| Detected Language | English |
| Type | PG_Thesis |
| Source | http://hub.hku.hk/bib/B47752993 |
| Rights | The author retains all proprietary rights, (such as patent rights) and the right to use in future works., Creative Commons: Attribution 3.0 Hong Kong License |
| Relation | HKU Theses Online (HKUTO) |
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