Component selection for exponential power mixture models
Xinyi Wang1, Zhenghui Feng1,2
1The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, People's Republic of China.
Abstract:
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.
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