Estimation methods in semiparametric regression

In this thesis, the semiparametric regression model that combines the best features of the parametric and the nonparametric approaches are introduced when the parametric model assumptions are violated. Three different approaches for the semiparametric regression model estimation are considered. Firstly, the smoothing spline estimation procedure based on penalized least squares is introduced and for the evaluation of a semiparametric model based on this procedure the smoothing parameter selection criteria are considered. Secondly, a wavelet based approach is introduced for estimating a semiparametric regression model. Finally the idea of differencing to the parameter estimation in semiparametric regression model is considered and a new difference-based estimator which is called difference-based ridge estimator when the presence of multicollinearity in the semiparametric regression model is suggested. The differencing estimator and difference-based ridge estimator are analyzed and compared in the sense of mean-squared error criterion.