Mean Squared Error For Optimal Designs in the Polynomial and Spline Regression
This thesis aims to further expand the existing optimal design theory for polynomial and spline regression models. We will show that the classical minimax design in polynomial regression models leads to the recently introduced stronger notion of R-optimality. Furthermore, we aim to clarify the notion of optimal design theory for spline regression models. We will describe various types of cardinal splines and discuss related to them various theorems within the context of optimal design.