Abstract: Data functionalizing is the basis of functional data analysis (FDA) and important step differed from other analysis methods.As the main approach of data functionalizing,data fitting usually can be converted into an optimization problem including loss function and the regularization term,and smoothing parameter plays a compromising role in weighing loss and the risk of over fitting.Generalized cross-validation (GCV) is a general and better parameter selection way,but massive calculation may be needed in order to get a more accurate smoothing parameter because GCV is calculated on discrete values.Aiming at this problem,the fitting optimization and the finite difference solution strategies were proposed to improve the solution efficiency of selection of the optimal smoothing parameter,and their precision and efficiency were compared and analyzed.The experiment results on simulated and real data sets demonstrate that the two proposed strategies are greatly improved in efficiency compared with the conventional grid method with almost the same precision.The finite difference solution strategy is better than the fitting optimization solution strategy in terms of algorithm precision,and the latter is more efficient.

Key words: Smoothing parameter,Generalized cross-validation,Finite difference solution strategy,Fitting optimization solution strategy