PhD Oral Presentation
In this thesis, we propose a model averaging estimation for the correlation structure of GEE model on longitudinal data and Bayesian nonparametric regression. Under the GEE framework we use a weighted sum of a group of patterned correlation matrices to estimate the correlation matrix. Consequently, a consistent and efficient estimator of the correlation structure can be found. For Bayesian nonparametric regression, we present a model averaging method to construct a prediction function in semiparametric form. The weighted sum of candidate semiparametric models is taken as a predictor of mean response. Marginal nonparametric regression models are approximated by spline basis functions and we apply a Bayesian Monte Carlo approach to fit such models. The optimal model weights are estimated by minimizing the least squares criterion with an explicit form. This methods is demonstrated to be more accurate than both classical parametric model averaging methods and existing semiparametric regression models. We implement our methods in extensive simulation studies and illustrate them with some real data examples.