Research On Robust Reression Method In Nonparametric Statistics

In the field of regression analysis,the least square method is widely used in practice,but its performance may be greatly reduced if the data set contains outliers or non-Gaussian noise.In this background,this paper studies a nonparametric regression method using a class of robust loss functions in the statistical learning framework.This type of loss function is defined by a window function and a scale parameter,and covers many commonly used regression loss functions.We will use the error decomposition method to analyze the generalization error of the algorithm and give the specific convergence rate.Through our analysis,we can see that the scale parameter in the loss function balance the convergence rate and robustness of the regression model.Combined with numerical experiments,we verify the effectiveness of the robust regression method.