Smoothing approaches in regression

This dissertation concerns the estimation of unknown smooth functions in semi-parametric regression models using smoothing approaches given longitudinal data or survival data.;In Chapter 2, we propose a class of semi-parametric quantile regression models for longitudinal data from the Bayesian point of view. We also provide an estimating procedure which is implemented in the standard software WinBUGS.;In Chapter 3, we study semi-parametric quantile regression models for longitudinal data with nonignorably missing covariates. In longitudinal data, it may happen that data are often missing and the missingness mechanism depends on the missing data (then said to be nonignorable). Our proposed estimating procedure can be conveniently implemented in WinBUGS.;In Chapter 4, we propose a class of partly linear transformation models, which includes the proportional hazards model and the proportional odds model as special cases, for survival data. We also suggest two estimating procedures based on local polynomial smoothing and penalized smoothing splines. Our estimating procedures are demonstrated through some simulations and real examples.;In Chapter 1, we review the research in the literature on smoothing and regressions. We also review quantile regression and survival analysis.;Chapter 5 concerns interval censored data. This type of data commonly arises in clinical trials and medical studies. The proportional hazards model and the proportional odds model are two popular models used in literature. We study a more flexible survival model via doubly penalized smoothing splines. Our proposed model allows some covariates to have nonlinear effects on the survival function of failure time.;Finally, Chapter 6 summarizes our work and addresses some aspects which remain to be completed.