Bayesian inference provides a flexible way of combiningg data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression ...

To effectively build a regression model with a large number of covariates is no easy task. We consider using dimension reduction before building a parametric or spline model. The dimension reduction procedure is based on ...

Microarray is a high throughput technology to measure the gene expression. Analysis of microarray data brings many interesting and challenging problems. This thesis consists three studies related to microarray data. First, ...

The Markov chain marginal bootstrap (MCMB) is a new bootstrap method proposed by He and Hu (2002) for constructing confidence intervals or regions based on likelihood equations. It is designed to ease the computational ...

Linear mixed models based on the normality assumption are widely used in health related studies. Although the normality assumption leads to simple, mathematically tractable, and powerful tests, violation of the assumption ...

Longitudinal data are characterized by repeated measures over time on each subject. The generalized estimating equations (GEE) approach (Liang and Zeger, 1996) has been widely used for the analysis of longitudinal data. ...

Traditional linear mixed effect models assume the distributions of the random effects and errors follow normal distribution with mean zero and homoscedastic variance sigma square. This thesis presents a new nonparametric ...

In this thesis, we consider a family of parametric power transformations for the dependent variable such that a linear or partially linear quantile regression model holds after transformation. The two models being considered ...

Quantile regression extends the statistical quantities of interest beyond conditional means. The regression has been well developed for linear models but less explored for nonparametric models. In this thesis, we consider ...

The well-known "curse of dimensionality" makes high-dimensional data analysis unusually challenging. Dimension reduction plays a valuable role in enabling certain statistical analyses performed in a parsimonious way. The ...