Change point estimation in standard process observed over time is an important problem in literature with applications in various fields. We study this problem in a heterogeneous population. A model-based clustering procedure relying on skewed matrix-variate mixture is proposed. It is capable of capturing the heterogeneity pattern and estimating change points from all data groups simultaneously. The appeal of such approach also lies in its flexibility to model the skewness and dependence in data with good interpretability. Two novel algorithms called matrix power mixture with abrupt change model and matrix power mixture with gradual change model are developed. The approaches are illustrated by simulation studies across a variety of settings. The models are then tested on the US crime data with promising results.

随着时间的推移，在标准过程中观察到的变化点估计是文献在各个领域中的重要问题。我们研究异质人口中的这个问题。提出了一种基于偏态矩阵-变量混合的基于模型的聚类过程。它能够捕获异构模式并同时从所有数据组估计变化点。这种方法的吸引力还在于它具有灵活性，可以很好地解释数据的偏度和依赖性。开发了两种新颖的算法，分别是具有突变模型的矩阵幂混合和具有渐变模型的矩阵幂混合。通过各种设置下的仿真研究说明了这些方法。然后在美国犯罪数据上对模型进行测试，结果令人鼓舞。