In this paper we consider functional data with heterogeneity in time and in population. We propose a mixture model with segmentation of time to represent this heterogeneity while keeping the functional structure. Maximum likelihood estimator is considered, proved to be identifiable and consistent. In practice, an EM algorithm is used, combined with dynamic programming for the maximization step, to approximate the maximum likelihood estimator. The method is illustrated on a simulated dataset, and used on a real dataset of electricity consumption.

翻译：本文考虑在时间与总体层面均存在异质性的函数型数据。我们提出一种融合时间分割机制的混合模型，在保持函数型结构的前提下表征这种异质性。采用极大似然估计方法，并证明其具有可识别性与相合性。实际应用中，将EM算法与动态规划相结合以实现极大似然估计的近似计算，其中动态规划用于求解最大化步骤。该方法在模拟数据集上进行了验证，并应用于真实电力消费数据集的分析。