基于稳健估计方法的线性回归研究  

Research of Linear Regression based on Robust Estimation

作　　者：王帅帅 徐凯[1] 孟凡芳[2] WANG Shuaishuai;XU Kai;MENG Fanfang(Qingdao Cigarette Factory,Qingdao,Shandong Province,266071 China;Qingdao Huanghai University,Qingdao,Shandong Province,266071 China)

机构地区：[1]青岛卷烟厂,山东青岛266071 [2]青岛黄海学院,山东青岛266071

出　　处：《科技创新导报》2021年第1期72-77,共6页Science and Technology Innovation Herald

摘　　要：基于最小二乘方法的线性回归估计方法,是通过最小化误差平方和寻找参数向量最优解,该方法对大的误差点不具稳健性。本文主要针对具有异常点的稳健估计方法,研究在背景噪声下的稳健估计性能,并通过数值仿真证明近似高斯分布,如高斯混合噪声模型下,单调型稳健M估计方法较好;在具有无穷方差的柯西背景噪声下,回降型M估计性能最优。理论和仿真实验均可得到稳健回归方法比最小二乘方法具有更好的稳健性。Based on the least squares estimation method of linear regression aims to f ind the optimal solution of the parameters by minimizing the sum of squared errors,which is not robust to large error points.Here,we focus on the robust estimation with outliers,investigating the performance of the robust estimation under various background noise.We prove that the monotone M-estimator shows a better performance under Gaussian mixed noise and the redescending M-estimator has a better eff iciency under Cauchy noise with inf inite variance.Both theory and simulation experiments show that the robust regression method has better robustness than the least square method.

关 键 词：线性回归 最小二乘法 稳健估计 M估计 稳健性 

分 类 号：O212.1[理学—概率论与数理统计]