正态分布混合线性专家模型的稳健估计  

Robust Estimation of Mixture of Linear Expert Model With Normal Distribution

作　　者：孙明云 李龙 Sun Mingyun;Li Long(College of Mathematics and Statistics,Hengyang Normal University,Hengyang Hunan 421002,China)

机构地区：[1]衡阳师范学院数学与统计学院,湖南衡阳421002

出　　处：《统计与决策》2025年第8期53-58,共6页Statistics & Decision

基　　金：湖南省自然科学基金资助项目(2025JJ70187);湖南省教育厅科学研究一般项目(22C0403);湖南省科技计划项目资助(2016TP1020);衡阳师范学院智能信息处理与应用湖南省重点实验室开放基金资助项目(2022HSK⁃FJJ014)。

摘　　要：针对误差项服从正态分布的混合线性专家模型(NMoLE模型)对异常值或重尾数据非常敏感的问题,文章提出了一种稳健估计方法:在NMoLE模型的对数似然函数中引入M估计,并提出了一种稳健的EM算法。蒙特卡洛模拟结果表明,所提稳健估计方法对带异常值的数据具有鲁棒性,且效果优于误差项服从t分布的混合线性专家模型的估计方法和极大似然估计方法;若数据中不存在异常值,则所提稳健估计方法与误差项服从t分布的混合线性专家模型的估计方法及极大似然估计方法的效果相近。最后,通过实际数据验证了所提估计方法的稳健性。Mixture of linear expert models with error terms following normal distribution(NMoLE)are very sensitive to outliers or heavy-tailed data.In view of this issue,the paper proposes a robust estimation method:Firstly,M estimation is introduced into the log-likelihood function of NMoLE model,and then a robust EM algorithm is proposed.Monte Carlo simulation results show that the proposed robust estimation is robust to the data with outliers,and is better than the mixture of linear expert model with error term following t-distribution and maximum likelihood estimation.If there are no outliers in the data,the results of robust estimation are not much different from those of the mixture of linear expert model with error term following t-distribution and maximum likelihood estimation.In addition,this paper successfully uses real data to illustrate the robustness of the proposed estimation method.

关 键 词：混合线性专家模型 NMoLE模型 M估计 

分 类 号：O212[理学—概率论与数理统计]