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：本文针对时间和群体层面均存在异质性的函数型数据开展研究。我们提出一种融合时间分割的混合模型，在保持函数型结构的同时刻画这种异质性。该模型的最大似然估计被证明具有可识别性和一致性。在实践层面，我们采用EM算法结合动态规划实现最大化步骤，以近似求解最大似然估计。通过模拟数据集验证该方法有效性，并将其应用于电力消费的真实数据集。