LTS回归与M估计稳健性的比较

Comparison of M estimator and LTS Estimator in Regression.

目的探讨可以同时抵抗回归数据中出现的Ｙ与Ｘ空间的多个异常点的稳健回归估计方法。方法介绍了Ｍ估计与ＬＴＳ估计，引入失效点的概念以讨论其稳健性尺度，并对两个模拟数据进行了分析比较。结果ＬＴＳ估计优于Ｍ估计，失效点较高。结论ＬＴＳ估计可同时抵抗Ｘ与Ｙ方面的异常。

Objective We will explore some robust regression estimates to resist multiple outliers from both sides.Methods We introduce M estimator and LTS estimator,with breakdown point to discuss their robustness.Also,we compare two simulated data as demonstration.Results LTS estimator is superior to M estimator,and has higher breakdown point.Conclusion LTS regression can resist outliers from both sides,and it is more robust.