Evaluating fit in functional data analysis using model embeddings

The author proposes a general method for evaluating the fit of a model for functional data. His approach consists of embedding the proposed model into a larger family of models, assuming the true process generating the data is within the larger family, and then computing a posterior distribution for the Kullback-Leibler distance between the true and the proposed models. The technique is illustrated on biomechanical data reported by Ramsay et al. (1995). It is developed in detail for hierarchical polynomial models such as those found in Lindley & Smith (1972), and is also generally applicable to longitudinal data analysis where polynomials are fit to many individuals.