We apply various variance reduction techniques to the estimation of Asian averages and options and propose an easy-to-use quasi-Monte Carlo method that can provide significant variance reductions with minimal increases in computational time. We have also extended these techniques to estimate higher moments of the Asians. We then use these estimated moments to efficiently implement Gram--Charlier based estimators for probability density functions of Asian averages and options. Finally, we investigate a ranking and selection application that uses post hoc analysis to determine how the circumstances of procedure termination affect the probability of correct selection.

Many applications of analysis of ranking data arise from different fields of study, such as psychology, economics, and politics. Over the past decade, many ranking data models have been proposed. AdaBoost is proved to be a very successful technique to generate a stronger classifier from weak ones; it can be viewed as a forward stagewise additive modeling using the exponential loss function. Motivated by this, a new AdaBoost algorithm is developed for ranking data. Taking into consideration the ordinal structure of the ranking data, I propose measures based on the Spearman/Kendall distance to evaluate classifier instead of the usual misclassification rate. Some ranking datasets are tested by the new algorithm, and the results show that the new algorithm outperforms traditional algorithms. The distance-based model assumes that the probability of observing a ranking depends on the distance between the ranking and its central ranking. Prediction of ranking data can be made by combining distance-based model with the famous k-nearest-neighbor (kNN) method. This model can be improved by assigning weights to the neighbors according to their distances to the central ranking and assigning weights to the features according to their relative importance. For the feature weighting part, a revised version of the traditional ReliefF algorithm is proposed. From the experimental results we can see that the new algorithm is more suitable for ranking data problem. Error-correcting output codes (ECOC) is widely used in solving multi-class learning problems by decomposing the multi-class problem into several binary classification problems. Several ECOCs for ranking data are proposed and tested. By combining these ECOCs and some traditional binary classifiers, a predictive model for ranking data with high accuracy can be made. While the mixture of factor analyzers (MFA) is useful tool for analyzing heterogeneous data, it cannot be directly used for ranking data due to the special discrete ordinal structures of rankings. I fill in this gap by extending MFA to accommodate for complete and incomplete/partial ranking data. Both simulated and real examples are studied to illustrate the effectiveness of the proposed MFA methods. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 89-95).

Thesis (M. Phil.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 94-102).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 224-227).

No description available.

General transformation models are a class of semiparametric survival models. The models generalize simple transformation models with more flexibility in modeling data coming from statistical practice. The models include many popular survival models as their special cases, e.g., proportional hazard Cox regression models, proportional odds models, generalized probit models, frailty survival models and heteroscedastic hazard regression models etc. Although the maximum marginal likelihood estimate of parameters in general transformation models with interval censored data is very satisfactory, its large sample properties are open. In this thesis, we will consider the problem and use discretization technique to establish the large sample properties of maximum marginal likelihood estimates with interval censored data. / In general, to reduce possible model bias, many covariates will be collected into a model. Hence a high-dimensional regression model is built. But at the same time, some non-significant variables may be also included in. So one of tasks to build an efficient survival model is to select significant variables. In this thesis, we will focus on the variable selection for general transformation models with ranking data, right censored data and interval censored data. Ranking data are widely seen in epidemiological studies, population pharmacokinetics and economics. Right censored data are the most common data in clinical trials. Interval censored data are another type common data in medical studies, financial, epidemiological, demographical and sociological studies. For example, a patient visits a doctor with a prespecified schedule. In his last visit, the doctor did not find occurrence of an interested event but at the current visit, the doctor found the event has occurred. Then the exact occurrence time of this event was censored in an interval bracketed by the two consecutive visiting dates. Based on rank-based penalized log-marginal likelihood approach, we will propose an uniform variable selection procedure for all three types of data mentioned above. In the penalized marginal likelihood function, we will consider non-concave and Adaptive-LASSO (ALASSO) penalties. For the non-concave penalties, we will adopt HARD thresholding, SCAD and LASSO penalties. ALASSO is an extended version of LASSO. The key of ALASSO is that it can assign weights to effects adaptively according to the importance of corresponding covariates. Therefore it has received more attention recently. By incorporating Monte Carlo Markov Chain stochastic approximation (MCMC-SA) algorithm, we also propose an uniform algorithm to find the rank-based penalized maximum marginal likelihood estimates. Based on the numeric approximation for marginal likelihood function, we propose two evaluation criteria---approximated GCV and BIC---to select proper tuning parameters. Using the procedure, we not only can select important variables but also be able to estimate corresponding effects simultaneously. An advantage of the proposed procedure is that it is baseline-free and censoring-distribution-free. With some regular conditions and proper penalties, we can establish the n -consistency and oracle properties of penalized maximum marginal likelihood estimates. We illustrate our proposed procedure by some simulations studies and some real data examples. At last, we will extend the procedures to analyze stratified survival data. / Keywords: General transformation models; Marginal likelihood; Ranking data; Right censored data; Interval censored data; Variable selection; HARD; SCAD; LASSO; ALASSO; Consistency; Oracle. / Li, Jianbo. / Adviser: Minggao Gu. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 104-111). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Chan, Ho Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 56). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Model --- p.3 / Chapter 3 --- Implementation by Mx --- p.10 / Chapter 3.1 --- Example 1 --- p.10 / Chapter 3.2 --- Example 2 --- p.22 / Chapter 4 --- Covariance structure analysis --- p.26 / Chapter 5 --- Simulation --- p.29 / Chapter 5.1 --- Simulation 1 --- p.29 / Chapter 5.2 --- Simulation 2 --- p.36 / Chapter 6 --- Discussion --- p.41 / Appendix A: Mx input script for ranking data data with p =4 --- p.43 / Appendix B: Selection matrices for ranking data with p = 4 --- p.47 / Appendix C: Mx input script for ranking data data with p = 3 --- p.50 / Appendix D: Mx input script for p = 4 with covariance structure --- p.53 / References --- p.56