{"title":"Component selection for exponential power mixture models.","authors":"Xinyi Wang, Zhenghui Feng","doi":"10.1080/02664763.2021.1990225","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":15239,"journal":{"name":"Journal of Applied Statistics","volume":"50 2","pages":"291-314"},"PeriodicalIF":1.2000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9870023/pdf/CJAS_50_1990225.pdf","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/02664763.2021.1990225","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
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.
指数幂族是一个非常灵活的分布族，其中高斯族是其子族。在本文中，我们研究了EP混合模型和回归的成分选择和估计。[X]中零分量均值的假设。曹庆，孟东，陈勇，徐志强，混合噪声下的鲁棒低秩矩阵分解，电子工程学报。反式。的形象。Process. 25 (2016)， pp. 4677-4690。是放松的。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缩小到零，从而实现成分的选择。提出了改进的电磁算法，得到了估计分量数的一致性。仿真研究表明，所提方法在组件数选择、参数估计和密度估计精度方面具有优势。本文给出了SHIBOR风险值分析和一个气候变化数据作为例证。
期刊介绍：
Journal of Applied Statistics provides a forum for communication between both applied statisticians and users of applied statistical techniques across a wide range of disciplines. These areas include business, computing, economics, ecology, education, management, medicine, operational research and sociology, but papers from other areas are also considered. The editorial policy is to publish rigorous but clear and accessible papers on applied techniques. Purely theoretical papers are avoided but those on theoretical developments which clearly demonstrate significant applied potential are welcomed. Each paper is submitted to at least two independent referees.
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