Quantile regression and survival analysis

The thesis consists of six chapters and focus on two topics: quantile regression and survival analysis. Firstly, direct use of regression quantiles to construct confidence intervals and confidence bands for conditional quantiles and prediction intervals for future response variables under homoscedastic linear models and heteroscedastic linear models is proposed. Comparison of the direct method with the studentization and the bootstrap methods are discussed in terms of computation and asymptotic theory. Simulation results show that the direct method has the advantage of robustness against departure from the normality assumption of the error terms. Next, the thesis discusses censored linear regression models and proposes two approaches which can be viewed as extensions of the two well-known estimators, one is proposed by Koul, Susarla and Van Ryzin (1981) and the one proposed by Buckley-James (1979). The results stated in the previous part may also be applied for censored data analysis. Asymptotic results and simulation results on the performance of the proposed methods with the use of linear programming algorithms and Splus functions are also presented. Finally, the cumulative logistic regression models are discussed. An example with the Veteran's lung cancer data is presented to illustrate the proposed method.U of I OnlyETDs are only available to UIUC Users without author permissio