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Research Projects Supported by HKU's High Performance Computing Facilities |
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| Researcher: |
| Miss Man-chi Pun, Department of Statistics and Actuarial Science |
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Project Title: |
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m out of n Bootstrap for Nonstandard M-Estimation |
| Project Description: |
| Nonstandard M-estimation, with nuisance parameters consistently estimated in the criterion function, often yields M-estimators converging weakly at rates different from n1/2. Their weak limits are typically non-Gaussian. The complicated asymptotics involved renders distributional estimation of the M-estimators analytically prohibitive. We show that the problem is resolved by m out of n bootstrapping under very general conditions, which provides a universal and convenient approach to consistently estimating sampling distributions of M-estimators. |
| Project Duration: |
| 2 years |
| Project Significance: |
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Making statistical inference of parameter is important in many statistical problems. Especially, the determination of an estimator for a particular parameter of interest and the evaluation of the accuracy of that estimator through estimates of the standard error of the estimator and the determination of confidence intervals are the two major problems in applied statistics. Accurate knowledge of sampling distributions helps us design reliable statistical procedures and make convincing inference. It provides a universal and convenient approach to consistently estimating sampling distributions of M-estimators. |
| Results Achieved: |
| We show that the problem is resolved by m out of n bootstrapping under very general conditions, which provides a universal and convenient approach to consistently estimating sampling distributions of M-estimators. Empirical evidence is provided by a simulation study to construct confidence intervals and to globally estimate sampling distributions of studentized location M-estimators and shorth estimators. |
| Remarks on the Use of High Performance Computing Cluster: |
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In this project, it required a large amount of simulation study, which provides empirical evidence of our findings by constructing confidence intervals and globally estimating sampling distributions. |