线性回归模型中参数估计稳健性比较及应用  

The Research on Robust Methods for Linear Regression and Application

作　　者：廖文辉 黄颖强 何志锋[1] 张健涛 戴浩然 李丹丹 LIAO Wen-hui;HUANG Ying-qiang;HE Zhi-feng;ZHANG Jian-tao;DAI Hao-ran;LI Dan-dan(Guangdong University of Finance,GuangZhou 510520,China;Huashang College of Guangdong,GuangZhou 510552,China;Department of Statistics,College of Economics,Jinan University,GuangZhou 510275,China;School of Mathematics Computational Science,SunYat-sen University,GuangZhou 510275,China)

机构地区：[1]广东金融学院,广东广州510520 [2]广州华商学院,广东广州510552 [3]暨南大学经济学院统计学系,广东广州510632 [4]中山大学数学学院,广东广州510275

出　　处：《数理统计与管理》2021年第5期822-832,共11页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(42077205);广东省自然科学基金项目(2018A030313171);全国统计科学研究项目(2017LY65).

摘　　要：线性回归模型中参数估计常用最小二乘法,该方法受离群值影响,而真实数据中离群点难以避免,这直接影响到线性回归模型的预测故果.稳健估计能有效地消除或减弱离群点对线性回归模型参数估计的影响.由于协方差矩阵是许多统计方法的基石,因此,最小协方差行列式估计成为常用稳健估计方法之一.本文针对最小协方差行列式估计获得均值和协方差估计的有效性不如罗克估计和合成似然估计,采用数值糢拟与真实数据预测,进一步对这三种技术获得参数估计进行稳健性比较.结果表明:合成似然估计与罗克估计表现更为稳徤,进而提出将其应用于大气污染物浓度预测。Ordinary Least sum of Square(OLS)was commonly used for parameter estimation of linear regression model,which was vulnerable and no robust.However,Outliers were difficult to avoid in real data,which affects the prediction effect of linear regression model.Robust estimation can effectively eliminate or weaken the influence of outliers in linear regression models.Since the covariance matrix was the cornerstone of many statistical methods,The MCD estimator became one of the common robust estimation methods.To this fact that the MCD estimator was not as good as Rocke estimator and SKMM estimator for the effectiveness of the mean and covariance estimation obtained.The robustness of the parameter estimation obtained by three techniques was further compared by using numerical simulation and real data prediction.The results show that Rocke estimator and SKMM estimator were more robust,and applied them to the concentration prediction of air pollutants.

关 键 词：稳健估计 最小协方差行列式估计 罗克估计 合成似然估计 线性回归模型 

分 类 号：O212[理学—概率论与数理统计]