Evaluating Fit in Functional Data Analysis Using Model Embeddings

Kert Viele

Abstract:

We propose a method for evaluating the fit of hierarchical polynomial models such as those found in Lindley and Smith (1972). The method consists of embedding a proposed polynomial into a larger family of models, assuming the true process generating the data is within the larger family, and then estimating the Kullback-Leibler information between the process generating the data and the proposed family. The method allows fit to be assessed both for a single curve and across a hierarchy of curves. For illustration, we evaluate the fit of a biomechanical model to pinch force data described in Ramsay, Flanagan, and Wang (1995).

Keywords: Curve Estimation, Goodness of Fit, Kullback-Leibler Information, Hierarchical Models, Model Embedding.

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