统计与决策2025，Vol.41Issue(11)：55-61,7.DOI:10.13546/j.cnki.tjyjc.2025.11.009
基于均值漂移惩罚的混合泊松回归模型的离群值检测与稳健推断
Outlier Detection and Robust Inference of Mixture Poisson Regression Models Based on Mean-shift Penalization
摘要
Abstract
When the dependent variable is a discrete random variable and follows the Poisson distribution,the Gaussian mix-ture regression model(GMRM)changes to a special kind of mixture Poisson regression model(MPRM).Based on the EM algorithm of the GMRM and the maximum likelihood estimation algorithm of the parameters of the ordinary Poisson regression model,this paper proposes the idea of combining the EM algorithm with the iterative reweighted least squares algorithm to estimate each pa-rameter of the mixture Poisson regression model.However,when outliers occur in the data,the mixture Poisson regression model and its algorithm cannot perform accurate parameter estimation.Therefore,a robust mixture Poisson regression model based on mean-shift penalization is further presented,and a thresholding embedded EM algorithm is designed.This model and its algorithm can simultaneously achieve accurate outlier detection and robust parameter estimation.The superiority of the proposed robust new method is verified by comparing it with the common Gaussian mixture regression model and the mixed Poisson regression model in data simulation analysis and empirical analysis.关键词
均值漂移惩罚/混合泊松回归模型/稳健推断/离群值检测Key words
mean-shift penalization/mixture Poisson regression model/robust inference/outlier detection分类
数学引用本文复制引用
余纯,黄丹..基于均值漂移惩罚的混合泊松回归模型的离群值检测与稳健推断[J].统计与决策,2025,41(11):55-61,7.基金项目
江西省自然科学基金资助项目(20202BABL201013) （20202BABL201013）
