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Semiparametric mixture regression with unspecified error distributions
TEST ( IF 1.3 ) Pub Date : 2020-07-08 , DOI: 10.1007/s11749-020-00725-z
Yanyuan Ma , Shaoli Wang , Lin Xu , Weixin Yao

In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal assumption is violated. By extending the semiparametric regression estimator proposed by Hunter and Young (J Nonparametr Stat 24:19–38, 2012a) which requires the component error densities to be the same (including homogeneous variance), we propose semiparametric mixture of linear regression models with unspecified component error distributions to reduce the modeling bias. We establish a more general identifiability result under weaker conditions than existing results, construct a class of new estimators, and establish their asymptotic properties. These asymptotic results also apply to many existing semiparametric mixture regression estimators whose asymptotic properties have remained unknown due to the inherent difficulties in obtaining them. Using simulation studies, we demonstrate the superiority of the proposed estimators over the MLE when the normal error assumption is violated and the comparability when the error is normal. Analysis of a newly collected Equine Infectious Anemia Virus data in 2017 is employed to illustrate the usefulness of the new estimator.



中文翻译:

具有不确定误差分布的半参数混合回归

在拟合线性回归模型的混合时,传统上使用正常假设对误差进行建模,然后由最大似然估计器(MLE)估计回归参数。如果违反正常假设,则此过程无效。通过扩展由Hunter和Young(J Nonparametr Stat 24:19–38,2012a)提出的半参数回归估计量,该估计方法要求分量误差密度相同(包括均方差),我们提出了线性回归模型与未指定分量的半参数混合误差分布以减少建模偏差。我们在比现有结果弱的条件下建立了更一般的可识别性结果,构造了一类新的估计量,并建立了它们的渐近性质。这些渐近结果还适用于许多现有的半参数混合回归估计量,由于其固有的困难性,其渐近性质仍然未知。通过仿真研究,我们证明了当违反正常误差假设时,建议的估计量优于MLE;当误差为正常值时,则具有可比性。分析了2017年新收集的马传染性贫血病毒数据,以说明新估算器的有用性。

更新日期:2020-07-09
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