| Research Projects Supported by HKU's High Performance Computing Facilities |
| ¡@ |
| Researcher: |
| Dr Stephen S M Lee, Department of Statistics and Actuarial Science |
| Project Title: |
| A Study of m out of n Bootstrap Procedures for General M-estimation |
| Project Description: |
| In the context of M-estimation, the bootstrap may be inconsistent in general situations where M-estimation arguably finds its most interesting applications. This project investigates the theoretical and practical effects of the m out of n bootstrap in general M-estimation problems, to which the method is anticipated to offer reliable solutions, and explores statistical applications made possible as a result of the investigation. Specifically, the m out of n bootstrap procedure will be established as an automatic and accurate means to assess general M-estimators, which is computationally straightforward and analytically undemanding on the part of practitioners, thus rendering itself very powerful and competitive among modern statistical methodologies. |
| Project Duration: |
| 3 years |
| Project Significance: |
|
On completion of this project, one can establish firmly the m out of n bootstrap as an important, automatic and universal procedure for making statistical inference based on general M-estimators, warn practitioners against possible misuse of the conventional bootstrap in the same context, and resolve the difficult problem of making practical use of the complicated asymptotic theory underlying general M-estimation. Such deliverables will lead to substantial enhancement of the power of M-estimation with full-blown availability of a rich class of M-estimators, and will find long-term impact in general statistical inference over a broad spectrum of applications. |
| Results Achieved: |
| We showed for M-estimation problems, with or without nuisance parameters, that the M-estimators, when appropriately centred and normed, converge weakly to maximizers of Gaussian processes under rather general conditions, and that the m out of n bootstrap is weakly consistent for the limit law under similar conditions. As an important application, we reviewed the asymptotics of regression Lp estimators under general classes of error densities. It was shown that the asymptotic distributions of Lp estimators depend crucially on p and the shape of the error density near the origin. Three research reports have been written up on the above findings. |
| Remarks on the Use of High Performance Computing Cluster: |
|
The project involves a huge
amount of Monte Carlo simulation, aimed at providing empirical support for
the theoretical findings and the proposed methodologies. The HPC Cluster, with its
high power and efficiency, provides an essential platform for implementation
of all the above empirical work. ¡@ |
| Email Address: |
| smslee@hkusua.hku.hk |