Identification of smoothing parameter values for functional data objects

Before functional data objects can be generated from the B-spline basis systems the degree of curve smoothing to be applied has to be determined. Following the process outlined in \cite{Ramsay_2009} a 'functional parameter object' that allows smoothness to be imposed on estimated functional parameters is now created (see section 5.2.4 of \cite{Ramsay_2009}). A functional data object is then created for the current model component using the new functional parameter object, along with an initial value of the smoothing parameter (\(\lambda\)). The degrees of freedom and generalised cross-validation criterion coefficient (see section 5.3 of \cite{Ramsay_2009}) can then be calculated for the current functional data object. By repeating this process for a range of \(\lambda\) values and plotting the results (see Fig. \ref{781086} to Fig. \ref{224241}) a suitable smoothing parameter can be identified that will be used in the final functional data object for each model component. An example of a smoothed functional data object generated for the number of corporations associated with different technologies in a given priority year is illustrated in Fig. \ref{405071} and Fig. \ref{135605}.