基于t函数的稳健变量选择方法

Robust Variable Selection Method Based on t Function

在已有研究的基础上,提出一种新的基于t函数的稳健变量选择方法.该方法通过惩罚估计方程中的惩罚函数达到变量选择的效果,方程中的权重矩阵和有界得分函数对自变量和因变量中的异常值有很好的限制作用,可同时达到稳健的变量选择和稳健估计.通过分析3种不同自由度的t函数性质,选取自由度为2的t函数,并与基于Huber函数的稳健变量选择方法进行比较.数值模拟结果表明,基于t函数的稳健变量选择方法在2种污染力度、3种污染方式的数据污染情况下,其稳健性均明显优于基于Huber函数的稳健变量选择方法.与参数估计效果相比,基于t函数的稳健变量选择方法优势更明显.

On the basis of existing research results,a new method for robust variable selection based on t function was proposed.The method achieves variable selection by the penalized function in the penalized estimating equation.Meanwhile,through the weight matrix and the bounded score function in the equation,the proposed method has a satisfactory resistance to outliers in independent variables and dependent variables,and can achieve the robust variable selection and estimation simultaneously.By analyzing the properties of t functions with3different kinds of degree of freedom,a t function with2degrees of freedom was used,and the method was compared with the Huber function based on robust variable selection method.The numerical simulation results show that,when data are contaminated with outliers by two kinds of contamination degree and three kinds of contamination mode,the proposed robust variable selection method based on t function performs better than that based on the Huber function,especially in variable selection.