B-spline smoothing and statistical inference for systems of differential equations

Traditional algorithms for modelling functional data use derivative-based optimisation methods to fit parameters. The process of finnding the derivatives of the fitting criterion with respect to the parameters is complex. In some cases, the derivatives might not exist everywhere, as is the case when the Mean Absolute Deviation criterion is used instead of the usual Least Squares approach. Accordingly, the use of derivative-free methods for Functional Data Analysis was investigated in this thesis. It was found that the derivative-free methods perform satisfactorily on simple FDA problems and that the implementation e ort was much less than for the derivative based methods. Furthermore, using derivative-free methods, it is possible to fit models using non-smooth loss functions such as the Mean Absolute Deviation criterion. It was also possible to fit a variety of parametric problems using a modified version of the derivative-free methodology developed in this thesis.