非参数异方差回归模型的局部多项式估计——基于农村居民消费与收入的实证分析

Local Polynomial Estimations for Non-parametric Heteroscedastic Regression Model——An Empirical Analysis of Rural Households' Consumption and Income

本文主要研究非参数异方差回归模型的局部多项式估计问题.首先利用局部线性逼近的技巧,得到了回归均值函数的局部极大似然估计.然后,考虑到回归方差函数的非负性,利用局部对数多项式拟合,得到了方差函数的局部多项式估计,保证了估计量的非负性,并证明了估计量的渐近性质.最后,通过对农村居民消费与收入的实证研究,说明了非参数异方差回归模型的局部多项式方法比普通最小二乘估计法的拟合效果更好,并且预测的精度更高.

This paper studied local polynomial estimations for non-parametric heteroscedastic regression models. First- ly, the local maximum likelihood estimation of regression mean function was gained by using local linear fitting. Secondly, con- sidering the positive of regression variance function, its local polynomial estimation was proposed by using local log-polynomial fitting, which guaranteed positive of the local estimation. Furthermore, we verified asymptotic normality of the local estima- tion. Finally, with the real data studies of Chinese rural residents＇ consumption and income, it shows that the local polynomial method for non-parametric regression models performs better than the least squares method, and has higher accuracy.