基于秩次的R类稳健回归

Rank-based Robust Regression Method

目的从参数估计、稳健性质、回归诊断应用等方面介绍基于广义秩次的一类稳健回归分析方法—R和GR估计。方法在SAS的IML模块下模拟其对非正态误差分布表现、正态误差下的估计效率并进行实例分析。结果误差为cauchy分布时,R估计优于LS估计,X空间存在离群值时,GR估计优于R和LS估计,误差为正态分布时,R与CR估计效率达95%。结论R和GR估计为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和Y空间离群点。

To explore the rank-based robust regression, R and GR estimator with their estimation methods, robustness properties and regression diagnostics. Methods Using SAS/IML, Simulation study were carried on under normal and nonormal distribution, and an medical research application were given. Results When errors Cauehy distributed, R estimator performs better than LS, when outliers occur in X space, GR estimator performs better than R and LS, when errors normal distributed, estimation efficiency of GR and R achieve 95 % or so. Conclusion R and GR estimators are efficient and robust, and GR estimator can resists outliers form both X and Y space.