基于LMS回归的一步M估计与加权最小二乘估计

探讨在GM假设条件不满足情况下对线性回归模型的稳健估计方法。方法：介绍了估计的稳健性尺度和有效性的概念，采用基于LMS估计的M估计及加权最小二乘估计做稳健回归。结果：通过对一个模拟数据的分析，说明这两种稳健估计结果均优于经典的M估计及LS估计。结论：本文介绍的两种估计方法同时具有较高的稳健性及有效性，并可作近似的稳健推断。

ONE-STEP M ESTIMATOR AND REWEIGHTED LEAST SQUARES ESTIMATOR BASED ON LEAST MEDIAN OF SQUARES REGRESSION

Objective: To explore robust linear regression estimates when GM condition is not hold for the model. Methods:We introduce the concept of robustness measure and efficiency of an estimator, then use LMS-based M estimator and reweightedleast squares estimator to fit the linear regression model. Results: The analysis of a simulated data shows that these two robust estimates are both super to the traditional M and LS estimates. Conclusions: The estimates we introduced combined both high robustness and high efficiency, and can be used to do some approxiate robust inference.