Non and semi-parametric regression with correlated data

This thesis consists of two parts. In chapter 2, we focus on optimal smoothing with correlated data and chapter 3 is devoted to marginal semiparametric modelling of longitudinal/clustered data. Penalized likelihood method offers versatile smoothing techniques in a variety of stochastic settings, and the proper selection of the smoothing parameters and other tuning parameters is crucial to the practical performance of penalized likelihood estimates. In chapter 2 of this thesis, we study the selection of the smoothing parameters and the correlation parameters in penalized likelihood regression with correlated data. We propose a simple modification of Mallows' CL to accommodate the correlation parameters, and derive a profiled version for use with unknown variance. The proposed methods are shown to be optimal in a certain sense through asymptotic analysis and numerical simulations. Real-data example is also presented and related issues discussed. As an extension of the first part, we consider the marginal semiparametric models for clustered and longitudinal data in chapter 3. We consider two estimation procedures, in which the nonparametric function is estimated using smoothing spline and propose a method to select the smoothing parameter. Asymptotic results are established under suitable assumptions. Empirical studies are carried out to compare finite sample performances of different methods.