一类基于秩次的稳健线性回归估计与诊断方法

A Rank-based Robust Linear Regression Analysis and Diagnostic Methods

线性回归模型的误差项不服从正态分布或存在多个离群点时,可以将残差秩次的某些函数作为权重引入估计模型来减少离群点的不良影响。本文从参数估计、稳健性质、回归诊断等方面对基于残差秩次的一类稳健回归方法进行介绍.通过模拟研究和实例分析表明,R和GR估计是一种估计效率较高的稳健回归方法,其中GR估计可同时避免X与Y空间离群点,而高失效点HBR估计可通过控制某个参数在稳健性与估计效率之间进行折衷.

When multiple outliers occur in linear regression model or the distribution of residuals is not normal, we can use residual＇s rank as weight function to get some resist estimator. In this paper, the estimation of parameter, robustness and diagnostic of theses rank-based regression are introduced. A limited Monte Carlo study and a data analysis show that R and GR estimators are efficient and robust, GR can resist outliers from both X and Y space, HBR estimator can get tradeoff between robustness and efficiency by specification of a parameter.