Roughness penalty approach in regression

In this thesis study, roughness penalty approach is examined by using smoothing spline and regression spline. Different algorithyms and convergence of those are studied for estimation of additive and generalized additive regression models. It is proved in the applications that the smoothing spline and regression spline methods are very important in complicated problems considering some explanotory variables have not linear effect on response variables. Obtaining a good model in roughness penalty approach in regression can be done by choosing the optimum smoothing parameter or appropriate degrees of freedom. Therefore some criteria about choosing the smoothing parameter and some defines of degrees of freedom are examined. It is shown that, when regression spline is used, roughness penalty method is more convenient in problems with large data input and multiple dimension. At the same time, it is observed that generalized additive models with thin plate spline can be beneficial. Keywords: Roughness penalty approach, Smoothing spline approach, Regression spline approach, Additive Model, Generalized additive model, Thin plate spline