This project centers on development of computationally intensive statistical procedures based on techniques such as the bootstrap, kernel smoothing, Markov Chain Monte Carlo, conditional sampling etc. and their applications to general inferences about quantiles and regression parameters.

One of the focuses is to develop an effective algorithm for confidence interval construction. Confidence interval is one of the major statistical techniques used in estimation problems. I intend to do this by an innovative method, which may be termed the iterated smoothed bootstrap. The bootstrap method is a computationally intensive statistical tool for solving various problems and has been modified to numerous versions. The project proposes to combine two types of modification, namely, the iterated and the smoothed bootstrap, to generate a new class of bootstrap confidence intervals.

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The analysis is divided into two parts, theoretical and practical. On the theoretical side, the asymptotic expansions for coverage probabilities of the proposed intervals were developed, which reveal the potential improvement achievable in the ideal situation where the sample size is sufficiently large. It has been successfully showed that the iterated smoothed bootstrap can play a constructive role in the subject area. On the practical side, a large-scale simulation study was carried out to investigate the small-sample performance of the method. The findings are encouraging.

Two research reports were written up, jointly with my supervisors, Dr. Stephen Lee and are now being reviewed by referred journals. Last summer, I won an international award, the IMS Laha Award, to present a paper at the Institute of Mathematical Statistical Meeting held in San Francisco.

In various large-scale simulation studies, the empirical findings were very encouraging and demonstrated the effectiveness of our computationally intensive methods. With the aid of Fortran programs performed on ‘supercomputers’ HPC Cluster provided by HKUCC, these studies were performed within reasonable time period. HPC Cluster’s powerful computational capacity has made a significant contribution to my work. I must say I have accumulated valuable technical skills in the subject area with the help and support from HKUCC

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