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.