Local functional data model for characterizing shape variation of similar curves

“Similar curves” in the present article refers to a family of curves whose major shape are similar, but who have variation coming from curve-specific sources. The goal here is to develop a general methodology to describe small changes among similar curves. Previous methods mainly focus on dimension reduction through FPCA, which are not appropriate for quantifying local variation. Here, we consider a local functional data model which divides data into segments adaptively and models each segment with a shape invariant model. Such model has great flexibility in characterizing local variation of curves, as illustrated by simulation and real data examples.