中文摘要：

函数型数据分析区别于多元数据分析的一个关键问题是不但需要考虑幅度变差，还要考虑相位变差（由翘曲函数描述）．翘曲函数的非参数估计不一定能有很好的解释，也不一定能相互比较．本文提出一个局部非线性参数模型，用参数来描述主要的局部变差，包括相位变差和幅度变差．这些参数具有可解释性，不同曲线的参数很容易相互比较．本文的模拟和实际数据分析进一步验证了此方法的优势．

英文摘要：

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.