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：本文研究在时间和群体上具有异质性的函数型数据。我们提出了一种结合时间分割的混合模型，以表征此类异质性同时保持函数结构。本文考虑了最大似然估计量，证明了其可识别性与一致性。实际应用中，采用EM算法并结合动态规划进行最大化步骤，以逼近最大似然估计量。该方法在模拟数据集上得到验证，并应用于真实的电力消费数据集。