一般回归模型中的非参数估计

NONPARAMETRIC ESTIMATION FOR A GENERAL, REGRESSION MODEL

本文考虑一般回归模型中回归系数的方向之估计。文中,利用最大似然型的准则,找到了回归系数方向的相合估计。但在把他们的估计中,对自变量的分布加上了很强的限制性条件。本文,为了去掉这个限制性条件,找到了一个非参数估计方法,并证明了它的相合性。

In this paper, the estimation of the direction of the regression ooeffcient of the general regression model is considered. Li and Duan use maximum likelihood type criteria to get a consistent series of estimators of the direction. The condition, which they imposed on the distribution of the regressor variable X in their construction of the estimators, is very restrictive. In this paper, to avoid the restrictive condition, a nonparametric estimator of the direction of the general regression model is constructed. The estimator is proved to be consistent.