Consistent nonparametric estimation of error distributions in linear model

For the linear modely _i =x _i +e _i ,i=1, 2 ···, let the error sequence {e _i } _i=1 be iid r.v.'s, with unknown densityf(x). In this paper, a nonparametric estimation method based on the residuals is proposed for estimatingf(x) and the consistency of the estimators is obtained.The project supported by National Natural Science Foundation of China Crant 18971061.