Local Nonlinear Parametric Model for Characterizing Shape of Functional Data

One key difference of analyzing functional data from multidimensional data is that one needs to take phase variation (described by warping functions) into consideration as well as amplitude variation. Nonparametric estimation of warping functions may not generate summary measures that are easily interpreted or compared. We propose a local nonlinear parametric model to capture major local variation including both phase variation and amplitude variation. The parameters are interpretable, and can be easily compared among different curves. Simulation and real data analysis are performed to illustrate the powerfulness of the method.