线性回归模型的非线性稳健估计——基于经验过程理论的研究

Nonlinear robust estimation of linear parametric regression models——Based on empirical process theory

线性回归模型参数估计的有效性及对厚尾扰动和离群值的稳健性有进一步改进的余地.本文基于条件分布函数提出线性参数模型的一种新的非线性稳健估计量,利用经验过程理论证明了其相合性和渐近正态性.相对于OLS(ordinary least squares)估计量和常用的稳健LAD(least absolute deviations)和Huber估计量,此估计量可全面把握因变量的分布信息,较准确地由样本数据反映真正的数据生成过程,关于扰动项的厚尾分布具有更好的稳健性,且可更好地消弱极端离群值样本对参数估计的不良影响.多种实验设计的模拟表明,此估计量在有限样本下表现良好;在厚尾扰动或离群值出现的时候,显示出良好的稳健性,且优于OLS、LAD以及Huber估计量的小样本表现.

There is room for improvement in the efficiency of parametric estimation for the linear regression model aud its robustness to heavy-tailed errors and outliers. This paper proposes an alternative robust regression nmthod based on conditional distribution function of the dependent variable, and proves the consistency and asymptotic normality of the proposed estimator by using empirical process theory. Compared with ordinary least squares （OLS） estimator and two other usual least absolute deviations （LAD） and Huber robust estimators, the proposed estimator can grasp the whole distribution information of the dependent wuiablc and lnore accurately uncover the true data generation process from the sample. It has better robuslness to the heavy-tailed distribution of the error term. It is immune to the outlying observa- tions and can be more easily weaken the bad effect of outliers on the parametric estimation. Simulation in various designs shows that the proposed estimator performs well in finite samples and is quite robust to the presence of heavy-tailed errors or outliers, and outperforms OLS, LAD and Huber estimators.