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Abstract:
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Modern technique allows recording data with high sample rate and generates various spiky functional data, such as EEG and mass spectrometry data data. To model the association between spiky functional data, one has to allow the existence of high local variations in the coefficient functions. However, the smoothing techniques in functional data analysis assume that the coefficient functions are smooth, which limits the types and magnitudes of local variations allowed in the coefficient functions. In this paper, we propose to model the coefficient functions in a much more general family of function spaces, where different levels of local variations are allowed in different spaces of this family. We propose a new regularization penalty to replace the traditional smoothness regularity. We apply the new frame work to our recently developed signal compression approach for function-on-function regression. In addition to ability to capture the association between high local variations, this method has good prediction performance and can handle multiple functional predictors with thousands of observation points.
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