Wang Xinyi, Feng Zhenghui
The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, People's Republic of China.
MOE Key Laboratory of Econometrics, Department of Statistics, School of Economics, Xiamen University, Xiamen, People's Republic of China.
J Appl Stat. 2021 Oct 22;50(2):291-314. doi: 10.1080/02664763.2021.1990225. eCollection 2023.
Exponential Power (EP) family is a much flexible distribution family including Gaussian family as a sub-family. In this article, we study component selection and estimation for EP mixture models and regressions. The assumption on zero component mean in [X. Cao, Q. Zhao, D. Meng, Y. Chen, and Z. Xu, Robust low-rank matrix factorization under general mixture noise distributions, IEEE. Trans. Image. Process. 25 (2016), pp. 4677-4690.] is relaxed. To select components and estimate parameters simultaneously, we propose a penalized likelihood method, which can shrink mixing proportions to zero to achieve components selection. Modified EM algorithms are proposed, and the consistency of estimated component number is obtained. Simulation studies show the advantages of the proposed methods on accuracies of component number selection, parameter estimation, and density estimation. Analysis of value at risk of SHIBOR and a climate change data are given as illustration.
指数幂（EP）族是一个非常灵活的分布族，高斯族是其子族。在本文中，我们研究了EP混合模型和回归的成分选择与估计。放宽了[X. Cao, Q. Zhao, D. Meng, Y. Chen, and Z. Xu, Robust low-rank matrix factorization under general mixture noise distributions, IEEE. Trans. Image. Process. 25 (2016), pp. 4677-4690.]中关于成分均值为零的假设。为了同时选择成分和估计参数，我们提出了一种惩罚似然方法，该方法可以将混合比例收缩至零以实现成分选择。提出了改进的期望最大化（EM）算法，并得到了估计成分数的一致性。仿真研究表明了所提方法在成分数选择、参数估计和密度估计精度方面的优势。给出了对上海银行间同业拆放利率（SHIBOR）风险价值的分析以及一个气候变化数据作为例证。
