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：本文研究了在时间和人群异质性存在的情况下函数数据。我们提出了一种混合模型，采用时间分割来表示异质性，同时保持函数结构。证明了最大似然估计器的可识别性和一致性。在实践中，我们采用EM算法，结合动态规划用于最大化步骤，来近似最大似然估计器。我们使用一个模拟数据集进行了方法演示，以及使用一个实际数据集（电力消耗数据集）进行了应用。