变量选择的稳健RMSq准则

Robust RMSq criterion of variable selection

提出变量选择准则RMSq的一种稳健形式，定义为R_RMSq＝R_RSSq／（n-q），其中R_RSSq＝∑ρ（rqi）是从选模型的稳健拟合中计算出的稳健残差和，当ρ（x）＝x^2／2时，R_RSSq即为最小二乘的残差平方和RSSq。由于RSSq易受异常情况的影响，当数据中存在异常值或误差不服从正态分布时，变量选择准则RMSq的性能将会变得很差，宜采用稳健的变量选择方法。模拟结果表明R_RMSq方法是有用的。

The paper presents a robust version of RMSq for regression variable selection. It' s defined byR-RMSq=R-RSSq/(n-q),where R_RSSq=∑ ρ (rqi) is the robust residual sum from a robust fit of the se-lected model. When ρ(x) =x^2/2,R-RSSq becomes the residual sum of squares (RSSq) of a least square fit.Because RSSq is easily affected by abnormal cases, in the presence of outliers and possible departures fromthe normality assumpution on the error distribution,the performance of RMSq criterion for variable selec-tion becomes very bad, and needs the use of robust version- Simulation results showed that the R-RMSqmethod is quite valuable.